LMFDB - Embedded newform 245.3.m.b.177.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,3,Mod(18,245)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 8]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("245.18");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	245.m (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.67576647683$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			177.3
Character	$\chi$	$=$	245.177
Dual form			245.3.m.b.18.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23172 + 0.330037i) q^{2} +(4.01589 + 1.07605i) q^{3} +(-2.05590 + 1.18698i) q^{4} +(1.75247 - 4.68282i) q^{5} -5.30157 q^{6} +(5.74725 - 5.74725i) q^{8} +(7.17525 + 4.14263i) q^{9} +O(q^{10})$	\(q+(-1.23172 + 0.330037i) q^{2} +(4.01589 + 1.07605i) q^{3} +(-2.05590 + 1.18698i) q^{4} +(1.75247 - 4.68282i) q^{5} -5.30157 q^{6} +(5.74725 - 5.74725i) q^{8} +(7.17525 + 4.14263i) q^{9} +(-0.613038 + 6.34629i) q^{10} +(2.98240 + 5.16566i) q^{11} +(-9.53353 + 2.55450i) q^{12} +(15.4106 - 15.4106i) q^{13} +(12.0767 - 16.9200i) q^{15} +(-0.434268 + 0.752174i) q^{16} +(0.226943 - 0.846962i) q^{17} +(-10.2051 - 2.73444i) q^{18} +(18.0198 + 10.4038i) q^{19} +(1.95549 + 11.7076i) q^{20} +(-5.37832 - 5.37832i) q^{22} +(3.12465 + 11.6614i) q^{23} +(29.2647 - 16.8960i) q^{24} +(-18.8577 - 16.4130i) q^{25} +(-13.8954 + 24.0675i) q^{26} +(-2.10122 - 2.10122i) q^{27} +7.52964i q^{29} +(-9.29084 + 24.8263i) q^{30} +(9.90283 + 17.1522i) q^{31} +(-8.12792 + 30.3338i) q^{32} +(6.41844 + 23.9539i) q^{33} +1.11811i q^{34} -19.6688 q^{36} +(13.4154 - 3.59463i) q^{37} +(-25.6289 - 6.86725i) q^{38} +(78.4697 - 45.3045i) q^{39} +(-16.8415 - 36.9853i) q^{40} -12.0569 q^{41} +(12.3503 - 12.3503i) q^{43} +(-12.2630 - 7.08007i) q^{44} +(31.9736 - 26.3406i) q^{45} +(-7.69736 - 13.3322i) q^{46} +(43.9302 - 11.7711i) q^{47} +(-2.55335 + 2.55335i) q^{48} +(28.6442 + 13.9924i) q^{50} +(1.82275 - 3.15710i) q^{51} +(-13.3907 + 49.9746i) q^{52} +(-9.78248 - 2.62121i) q^{53} +(3.28158 + 1.89462i) q^{54} +(29.4164 - 4.91337i) q^{55} +(61.1707 + 61.1707i) q^{57} +(-2.48506 - 9.27437i) q^{58} +(-18.2765 + 10.5519i) q^{59} +(-4.74494 + 49.1206i) q^{60} +(15.1204 - 26.1893i) q^{61} +(-17.8583 - 17.8583i) q^{62} -43.5193i q^{64} +(-45.1584 - 99.1715i) q^{65} +(-15.8114 - 27.3861i) q^{66} +(-18.6717 + 69.6836i) q^{67} +(0.538751 + 2.01065i) q^{68} +50.1930i q^{69} -128.667 q^{71} +(65.0467 - 17.4292i) q^{72} +(-72.5481 - 19.4392i) q^{73} +(-15.3375 + 8.85513i) q^{74} +(-58.0691 - 86.2048i) q^{75} -49.3961 q^{76} +(-81.7002 + 81.7002i) q^{78} +(-14.8579 - 8.57820i) q^{79} +(2.76126 + 3.35176i) q^{80} +(-43.4609 - 75.2765i) q^{81} +(14.8507 - 3.97924i) q^{82} +(-4.42198 + 4.42198i) q^{83} +(-3.56846 - 2.54701i) q^{85} +(-11.1360 + 19.2881i) q^{86} +(-8.10230 + 30.2382i) q^{87} +(46.8289 + 12.5478i) q^{88} +(-94.1599 - 54.3633i) q^{89} +(-30.6890 + 42.9966i) q^{90} +(-20.2657 - 20.2657i) q^{92} +(21.3120 + 79.5373i) q^{93} +(-50.2247 + 28.9972i) q^{94} +(80.2982 - 66.1515i) q^{95} +(-65.2816 + 113.071i) q^{96} +(55.4317 + 55.4317i) q^{97} +49.4198i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 2 q^{3} + 4 q^{5} - 36 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 + 2 * q^3 + 4 * q^5 - 36 * q^8	$ 24 q - 2 q^{2} + 2 q^{3} + 4 q^{5} - 36 q^{8} - 14 q^{10} - 24 q^{11} + 46 q^{12} + 8 q^{13} + 52 q^{15} + 20 q^{16} + 48 q^{17} - 4 q^{18} + 72 q^{20} + 104 q^{22} - 86 q^{23} - 16 q^{25} - 140 q^{26} - 76 q^{27} + 64 q^{30} - 120 q^{31} + 130 q^{32} - 116 q^{33} - 496 q^{36} + 44 q^{37} - 16 q^{38} + 158 q^{40} - 16 q^{41} - 196 q^{43} + 104 q^{45} - 148 q^{46} + 208 q^{47} + 52 q^{48} + 580 q^{50} - 160 q^{51} + 288 q^{52} - 72 q^{53} - 208 q^{55} + 656 q^{57} - 2 q^{58} + 262 q^{60} - 308 q^{61} - 176 q^{62} + 132 q^{65} - 316 q^{66} + 198 q^{67} - 332 q^{68} - 792 q^{71} + 308 q^{72} - 380 q^{73} + 450 q^{75} + 400 q^{76} - 720 q^{78} + 324 q^{80} - 352 q^{81} + 818 q^{82} + 460 q^{83} + 144 q^{85} - 336 q^{86} + 214 q^{87} - 288 q^{88} - 120 q^{90} + 1372 q^{92} - 68 q^{93} - 88 q^{95} - 816 q^{96} + 72 q^{97}+O(q^{100}) $ 24 * q - 2 * q^2 + 2 * q^3 + 4 * q^5 - 36 * q^8 - 14 * q^10 - 24 * q^11 + 46 * q^12 + 8 * q^13 + 52 * q^15 + 20 * q^16 + 48 * q^17 - 4 * q^18 + 72 * q^20 + 104 * q^22 - 86 * q^23 - 16 * q^25 - 140 * q^26 - 76 * q^27 + 64 * q^30 - 120 * q^31 + 130 * q^32 - 116 * q^33 - 496 * q^36 + 44 * q^37 - 16 * q^38 + 158 * q^40 - 16 * q^41 - 196 * q^43 + 104 * q^45 - 148 * q^46 + 208 * q^47 + 52 * q^48 + 580 * q^50 - 160 * q^51 + 288 * q^52 - 72 * q^53 - 208 * q^55 + 656 * q^57 - 2 * q^58 + 262 * q^60 - 308 * q^61 - 176 * q^62 + 132 * q^65 - 316 * q^66 + 198 * q^67 - 332 * q^68 - 792 * q^71 + 308 * q^72 - 380 * q^73 + 450 * q^75 + 400 * q^76 - 720 * q^78 + 324 * q^80 - 352 * q^81 + 818 * q^82 + 460 * q^83 + 144 * q^85 - 336 * q^86 + 214 * q^87 - 288 * q^88 - 120 * q^90 + 1372 * q^92 - 68 * q^93 - 88 * q^95 - 816 * q^96 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.23172	+	0.330037i	−0.615858	+	0.165019i	−0.553244	−	0.833019i	$-0.686610\pi$
$2$	−1.23172	+	0.330037i	−0.615858	+	0.165019i	−0.0626137	+	0.998038i	$0.519944\pi$
$3$	4.01589	+	1.07605i	1.33863	+	0.358685i	0.855926	−	0.517099i	$-0.172988\pi$
$3$	4.01589	+	1.07605i	1.33863	+	0.358685i	0.482704	+	0.875784i	$0.339655\pi$
$4$	−2.05590	+	1.18698i	−0.513976	+	0.296744i
$5$	1.75247	−	4.68282i	0.350494	−	0.936565i
$5$	1.75247	−	4.68282i	0.350494	−	0.936565i
$6$	−5.30157			−0.883595
$7$		0			0
$7$		0			0
$8$	5.74725	−	5.74725i	0.718407	−	0.718407i
$9$	7.17525	+	4.14263i	0.797250	+	0.460292i
$10$	−0.613038	+	6.34629i	−0.0613038	+	0.634629i
$11$	2.98240	+	5.16566i	0.271127	+	0.469605i	0.969151	−	0.246469i	$-0.0792704\pi$
$11$	2.98240	+	5.16566i	0.271127	+	0.469605i	−0.698024	+	0.716075i	$0.745937\pi$
$12$	−9.53353	+	2.55450i	−0.794461	+	0.212875i
$13$	15.4106	−	15.4106i	1.18543	−	1.18543i	0.207110	−	0.978318i	$-0.433594\pi$
$13$	15.4106	−	15.4106i	1.18543	−	1.18543i	0.978318	−	0.207110i	$-0.0664058\pi$
$14$		0			0
$15$	12.0767	−	16.9200i	0.805113	−	1.12800i
$16$	−0.434268	+	0.752174i	−0.0271418	+	0.0470109i
$17$	0.226943	−	0.846962i	0.0133496	−	0.0498213i	−0.958930	−	0.283644i	$-0.908457\pi$
$17$	0.226943	−	0.846962i	0.0133496	−	0.0498213i	0.972279	+	0.233822i	$0.0751234\pi$
$18$	−10.2051	−	2.73444i	−0.566949	−	0.151914i
$19$	18.0198	+	10.4038i	0.948412	+	0.547566i	0.892587	−	0.450874i	$-0.148888\pi$
$19$	18.0198	+	10.4038i	0.948412	+	0.547566i	0.0558250	+	0.998441i	$0.482221\pi$
$20$	1.95549	+	11.7076i	0.0977747	+	0.585379i
$21$		0			0
$22$	−5.37832	−	5.37832i	−0.244469	−	0.244469i
$23$	3.12465	+	11.6614i	0.135854	+	0.507015i	0.999993	+	0.00376143i	$0.00119730\pi$
$23$	3.12465	+	11.6614i	0.135854	+	0.507015i	−0.864139	+	0.503254i	$0.832136\pi$
$24$	29.2647	−	16.8960i	1.21936	−	0.703999i
$25$	−18.8577	−	16.4130i	−0.754308	−	0.656521i
$26$	−13.8954	+	24.0675i	−0.534437	+	0.925672i
$27$	−2.10122	−	2.10122i	−0.0778228	−	0.0778228i
$28$		0			0
$29$			7.52964i			0.259643i	0.991537	+	0.129821i	$0.0414404\pi$
$29$			7.52964i			0.259643i	−0.991537	+	0.129821i	$0.958560\pi$
$30$	−9.29084	+	24.8263i	−0.309695	+	0.827544i
$31$	9.90283	+	17.1522i	0.319446	+	0.553297i	0.980373	−	0.197154i	$-0.0631698\pi$
$31$	9.90283	+	17.1522i	0.319446	+	0.553297i	−0.660926	+	0.750451i	$0.729836\pi$
$32$	−8.12792	+	30.3338i	−0.253997	+	0.947931i
$33$	6.41844	+	23.9539i	0.194498	+	0.725877i
$34$			1.11811i			0.0328857i
$35$		0			0
$36$	−19.6688			−0.546356
$37$	13.4154	−	3.59463i	0.362577	−	0.0971523i	−0.0729310	−	0.997337i	$-0.523235\pi$
$37$	13.4154	−	3.59463i	0.362577	−	0.0971523i	0.435508	+	0.900185i	$0.356569\pi$
$38$	−25.6289	−	6.86725i	−0.674446	−	0.180717i
$39$	78.4697	−	45.3045i	2.01204	−	1.16165i
$40$	−16.8415	−	36.9853i	−0.421037	−	0.924632i
$41$	−12.0569			−0.294072			−0.147036	−	0.989131i	$-0.546973\pi$
$41$	−12.0569			−0.294072			−0.147036	+	0.989131i	$0.546973\pi$
$42$		0			0
$43$	12.3503	−	12.3503i	0.287215	−	0.287215i	−0.548763	−	0.835978i	$-0.684901\pi$
$43$	12.3503	−	12.3503i	0.287215	−	0.287215i	0.835978	+	0.548763i	$0.184901\pi$
$44$	−12.2630	−	7.08007i	−0.278705	−	0.160911i
$45$	31.9736	−	26.3406i	0.710525	−	0.585346i
$46$	−7.69736	−	13.3322i	−0.167334	−	0.289831i
$47$	43.9302	−	11.7711i	0.934686	−	0.250448i	0.240834	−	0.970566i	$-0.422579\pi$
$47$	43.9302	−	11.7711i	0.934686	−	0.250448i	0.693852	+	0.720118i	$0.255912\pi$
$48$	−2.55335	+	2.55335i	−0.0531949	+	0.0531949i
$49$		0			0
$50$	28.6442	+	13.9924i	0.572884	+	0.279849i
$51$	1.82275	−	3.15710i	0.0357403	−	0.0619039i
$52$	−13.3907	+	49.9746i	−0.257513	+	0.961050i
$53$	−9.78248	−	2.62121i	−0.184575	−	0.0494567i	0.165348	−	0.986235i	$-0.447125\pi$
$53$	−9.78248	−	2.62121i	−0.184575	−	0.0494567i	−0.349923	+	0.936779i	$0.613792\pi$
$54$	3.28158	+	1.89462i	0.0607700	+	0.0350856i
$55$	29.4164	−	4.91337i	0.534844	−	0.0893340i
$56$		0			0
$57$	61.1707	+	61.1707i	1.07317	+	1.07317i
$58$	−2.48506	−	9.27437i	−0.0428459	−	0.159903i
$59$	−18.2765	+	10.5519i	−0.309771	+	0.178847i	−0.646824	−	0.762639i	$-0.723903\pi$
$59$	−18.2765	+	10.5519i	−0.309771	+	0.178847i	0.337053	+	0.941486i	$0.390570\pi$
$60$	−4.74494	+	49.1206i	−0.0790824	+	0.818676i
$61$	15.1204	−	26.1893i	0.247876	−	0.429333i	−0.715061	−	0.699062i	$-0.753601\pi$
$61$	15.1204	−	26.1893i	0.247876	−	0.429333i	0.962936	+	0.269729i	$0.0869343\pi$
$62$	−17.8583	−	17.8583i	−0.288038	−	0.288038i
$63$		0			0
$64$		−	43.5193i		−	0.679988i
$65$	−45.1584	−	99.1715i	−0.694745	−	1.52572i
$66$	−15.8114	−	27.3861i	−0.239566	−	0.414941i
$67$	−18.6717	+	69.6836i	−0.278682	+	1.04005i	0.674652	+	0.738136i	$0.264294\pi$
$67$	−18.6717	+	69.6836i	−0.278682	+	1.04005i	−0.953334	+	0.301918i	$0.902373\pi$
$68$	0.538751	+	2.01065i	0.00792281	+	0.0295683i
$69$			50.1930i			0.727435i
$70$		0			0
$71$	−128.667			−1.81222			−0.906108	−	0.423047i	$-0.860960\pi$
$71$	−128.667			−1.81222			−0.906108	+	0.423047i	$0.860960\pi$
$72$	65.0467	−	17.4292i	0.903427	−	0.242072i
$73$	−72.5481	−	19.4392i	−0.993810	−	0.266290i	−0.274960	−	0.961456i	$-0.588665\pi$
$73$	−72.5481	−	19.4392i	−0.993810	−	0.266290i	−0.718850	+	0.695165i	$0.755331\pi$
$74$	−15.3375	+	8.85513i	−0.207264	+	0.119664i
$75$	−58.0691	−	86.2048i	−0.774255	−	1.14940i
$76$	−49.3961			−0.649948
$77$		0			0
$78$	−81.7002	+	81.7002i	−1.04744	+	1.04744i
$79$	−14.8579	−	8.57820i	−0.188074	−	0.108585i	0.403006	−	0.915197i	$-0.367965\pi$
$79$	−14.8579	−	8.57820i	−0.188074	−	0.108585i	−0.591081	+	0.806612i	$0.701299\pi$
$80$	2.76126	+	3.35176i	0.0345157	+	0.0418971i
$81$	−43.4609	−	75.2765i	−0.536554	−	0.929339i
$82$	14.8507	−	3.97924i	0.181106	−	0.0485273i
$83$	−4.42198	+	4.42198i	−0.0532769	+	0.0532769i	−0.733243	−	0.679966i	$-0.761994\pi$
$83$	−4.42198	+	4.42198i	−0.0532769	+	0.0532769i	0.679966	+	0.733243i	$0.261994\pi$
$84$		0			0
$85$	−3.56846	−	2.54701i	−0.0419819	−	0.0299648i
$86$	−11.1360	+	19.2881i	−0.129488	+	0.224280i
$87$	−8.10230	+	30.2382i	−0.0931299	+	0.347565i
$88$	46.8289	+	12.5478i	0.532147	+	0.142588i
$89$	−94.1599	−	54.3633i	−1.05798	−	0.610823i	−0.133105	−	0.991102i	$-0.542495\pi$
$89$	−94.1599	−	54.3633i	−1.05798	−	0.610823i	−0.924872	+	0.380279i	$0.875828\pi$
$90$	−30.6890	+	42.9966i	−0.340989	+	0.477740i
$91$		0			0
$92$	−20.2657	−	20.2657i	−0.220280	−	0.220280i
$93$	21.3120	+	79.5373i	0.229161	+	0.855240i
$94$	−50.2247	+	28.9972i	−0.534305	+	0.308481i
$95$	80.2982	−	66.1515i	0.845244	−	0.696331i
$96$	−65.2816	+	113.071i	−0.680017	+	1.17782i
$97$	55.4317	+	55.4317i	0.571461	+	0.571461i	0.932537	−	0.361076i	$-0.117590\pi$
$97$	55.4317	+	55.4317i	0.571461	+	0.571461i	−0.361076	+	0.932537i	$0.617590\pi$
$98$		0			0
$99$			49.4198i			0.499190i
$100$	58.2515	+	11.3599i	0.582515	+	0.113599i
$101$	−80.0618	−	138.671i	−0.792691	−	1.37298i	−0.924295	−	0.381678i	$-0.875346\pi$
$101$	−80.0618	−	138.671i	−0.792691	−	1.37298i	0.131605	−	0.991302i	$-0.457987\pi$
$102$	−1.20315	+	4.49023i	−0.0117956	+	0.0440218i
$103$	32.1500	+	119.986i	0.312136	+	1.16491i	0.926626	+	0.375984i	$0.122695\pi$
$103$	32.1500	+	119.986i	0.312136	+	1.16491i	−0.614490	+	0.788925i	$0.710638\pi$
$104$		−	177.137i		−	1.70324i
$105$		0			0
$106$	12.9143			0.121833
$107$	−130.359	+	34.9296i	−1.21831	+	0.326445i	−0.810017	−	0.586407i	$-0.800542\pi$
$107$	−130.359	+	34.9296i	−1.21831	+	0.326445i	−0.408292	+	0.912852i	$0.633875\pi$
$108$	6.81399	+	1.82580i	0.0630925	+	0.0169056i
$109$	−113.564	+	65.5664i	−1.04187	+	0.601527i	−0.920364	−	0.391064i	$-0.872107\pi$
$109$	−113.564	+	65.5664i	−1.04187	+	0.601527i	−0.121511	+	0.992590i	$0.538774\pi$
$110$	−34.6111	+	15.7604i	−0.314646	+	0.143276i
$111$	57.7426			0.520204
$112$		0			0
$113$	−54.8723	+	54.8723i	−0.485596	+	0.485596i	−0.906913	−	0.421317i	$-0.861568\pi$
$113$	−54.8723	+	54.8723i	−0.485596	+	0.485596i	0.421317	+	0.906913i	$0.361568\pi$
$114$	−95.5334	−	55.1562i	−0.838013	−	0.483827i
$115$	60.0839	+	5.80398i	0.522469	+	0.0504694i
$116$	−8.93750	−	15.4802i	−0.0770474	−	0.133450i
$117$	174.415	−	46.7343i	1.49072	−	0.399439i
$118$	19.0289	−	19.0289i	0.161262	−	0.161262i
$119$		0			0
$120$	−27.8354	−	166.651i	−0.231962	−	1.38876i
$121$	42.7106	−	73.9770i	0.352980	−	0.611380i
$122$	−9.98059	+	37.2481i	−0.0818081	+	0.305312i
$123$	−48.4193	−	12.9739i	−0.393653	−	0.105479i
$124$	−40.7185	−	23.5088i	−0.328375	−	0.189587i
$125$	−109.907	+	59.5440i	−0.879255	+	0.476352i
$126$		0			0
$127$	119.378	+	119.378i	0.939985	+	0.939985i	0.998298	−	0.0583136i	$-0.0185723\pi$
$127$	119.378	+	119.378i	0.939985	+	0.939985i	−0.0583136	+	0.998298i	$0.518572\pi$
$128$	−18.1487	−	67.7318i	−0.141787	−	0.529155i
$129$	62.8868	−	36.3077i	0.487495	−	0.281455i
$130$	88.3526	+	107.247i	0.679635	+	0.824978i
$131$	25.8642	−	44.7981i	0.197437	−	0.341970i	−0.750260	−	0.661143i	$-0.770072\pi$
$131$	25.8642	−	44.7981i	0.197437	−	0.341970i	0.947697	+	0.319173i	$0.103405\pi$
$132$	−41.6285	−	41.6285i	−0.315367	−	0.315367i
$133$		0			0
$134$		−	91.9927i		−	0.686513i
$135$	−13.5219	+	6.15731i	−0.100163	+	0.0456097i
$136$	−3.56341	−	6.17200i	−0.0262015	−	0.0453824i
$137$	50.6274	−	188.944i	0.369543	−	1.37915i	−0.491614	−	0.870813i	$-0.663593\pi$
$137$	50.6274	−	188.944i	0.369543	−	1.37915i	0.861157	−	0.508339i	$-0.169740\pi$
$138$	−16.5656	−	61.8235i	−0.120040	−	0.447996i
$139$			127.517i			0.917386i	0.888595	+	0.458693i	$0.151682\pi$
$139$			127.517i			0.917386i	−0.888595	+	0.458693i	$0.848318\pi$
$140$		0			0
$141$	189.085			1.34103
$142$	158.481	−	42.4650i	1.11607	−	0.299049i
$143$	125.566	+	33.6453i	0.878085	+	0.235282i
$144$	−6.23196	+	3.59802i	−0.0432775	+	0.0249863i
$145$	35.2600	+	13.1955i	0.243172	+	0.0910032i
$146$	95.7743			0.655988
$147$		0			0
$148$	−23.3139	+	23.3139i	−0.157527	+	0.157527i
$149$	192.034	+	110.871i	1.28882	+	0.744100i	0.978444	−	0.206514i	$-0.0662120\pi$
$149$	192.034	+	110.871i	1.28882	+	0.744100i	0.310375	+	0.950614i	$0.399545\pi$
$150$	99.9754	+	87.0148i	0.666503	+	0.580099i
$151$	33.2375	+	57.5691i	0.220116	+	0.381252i	0.954843	−	0.297111i	$-0.0960231\pi$
$151$	33.2375	+	57.5691i	0.220116	+	0.381252i	−0.734727	+	0.678363i	$0.762690\pi$
$152$	163.358	−	43.7715i	1.07472	−	0.287971i
$153$	5.13702	−	5.13702i	0.0335753	−	0.0335753i
$154$		0			0
$155$	97.6752	−	16.3145i	0.630162	−	0.105255i
$156$	−107.551	+	186.283i	−0.689428	+	1.19412i
$157$	−24.9966	+	93.2888i	−0.159214	+	0.594196i	0.839493	+	0.543370i	$0.182852\pi$
$157$	−24.9966	+	93.2888i	−0.159214	+	0.594196i	−0.998708	+	0.0508258i	$0.983815\pi$
$158$	21.1318	+	5.66225i	0.133746	+	0.0358370i
$159$	−36.4648	−	21.0530i	−0.229338	−	0.132409i
$160$	127.804	+	91.2207i	0.798774	+	0.570129i
$161$		0			0
$162$	78.3755	+	78.3755i	0.483799	+	0.483799i
$163$	11.1914	+	41.7669i	0.0686589	+	0.256238i	0.991721	−	0.128413i	$-0.0409883\pi$
$163$	11.1914	+	41.7669i	0.0686589	+	0.256238i	−0.923062	+	0.384651i	$0.874322\pi$
$164$	24.7879	−	14.3113i	0.151146	−	0.0872641i
$165$	123.420	+	11.9221i	0.748001	+	0.0722554i
$166$	3.98720	−	6.90604i	0.0240193	−	0.0416026i
$167$	−133.439	−	133.439i	−0.799038	−	0.799038i	0.183906	−	0.982944i	$-0.441126\pi$
$167$	−133.439	−	133.439i	−0.799038	−	0.799038i	−0.982944	+	0.183906i	$0.941126\pi$
$168$		0			0
$169$		−	305.971i		−	1.81048i
$170$	5.23594	+	1.95946i	0.0307996	+	0.0115263i
$171$	86.1978	+	149.299i	0.504081	+	0.873094i
$172$	−10.7315	+	40.0504i	−0.0623923	+	0.232851i
$173$	57.9299	+	216.197i	0.334855	+	1.24970i	0.904026	+	0.427477i	$0.140598\pi$
$173$	57.9299	+	216.197i	0.334855	+	1.24970i	−0.569171	+	0.822219i	$0.692736\pi$
$174$		−	39.9189i		−	0.229419i
$175$		0			0
$176$	−5.18064			−0.0294354
$177$	−84.7509	+	22.7089i	−0.478819	+	0.128299i
$178$	133.920	+	35.8838i	0.752360	+	0.201594i
$179$	−78.9406	+	45.5764i	−0.441009	+	0.254617i	−0.704026	−	0.710175i	$-0.748616\pi$
$179$	−78.9406	+	45.5764i	−0.441009	+	0.254617i	0.263016	+	0.964791i	$0.415283\pi$
$180$	−34.4690	+	92.1056i	−0.191495	+	0.511698i
$181$	146.339			0.808505			0.404253	−	0.914647i	$-0.367532\pi$
$181$	146.339			0.808505			0.404253	+	0.914647i	$0.367532\pi$
$182$		0			0
$183$	88.9030	−	88.9030i	0.485809	−	0.485809i
$184$	84.9789	+	49.0626i	0.461842	+	0.266645i
$185$	6.67697	−	69.1213i	0.0360917	−	0.373628i
$186$	−52.5005	−	90.9336i	−0.282261	−	0.488890i
$187$	5.05195	−	1.35367i	0.0270158	−	0.00723885i
$188$	−76.3443	+	76.3443i	−0.406087	+	0.406087i
$189$		0			0
$190$	−77.0721	+	107.981i	−0.405643	+	0.568322i
$191$	−42.2285	+	73.1419i	−0.221092	+	0.382942i	−0.955140	−	0.296156i	$-0.904295\pi$
$191$	−42.2285	+	73.1419i	−0.221092	+	0.382942i	0.734048	+	0.679097i	$0.237629\pi$
$192$	46.8291	−	174.769i	0.243901	−	0.910253i
$193$	−104.151	−	27.9071i	−0.539641	−	0.144596i	−0.0213045	−	0.999773i	$-0.506782\pi$
$193$	−104.151	−	27.9071i	−0.539641	−	0.144596i	−0.518337	+	0.855177i	$0.673449\pi$
$194$	−86.5706	−	49.9816i	−0.446240	−	0.257637i
$195$	−74.6372	−	446.855i	−0.382755	−	2.29156i
$196$		0			0
$197$	−49.0877	−	49.0877i	−0.249176	−	0.249176i	0.571456	−	0.820633i	$-0.306379\pi$
$197$	−49.0877	−	49.0877i	−0.249176	−	0.249176i	−0.820633	+	0.571456i	$0.806379\pi$
$198$	−16.3104	−	60.8712i	−0.0823757	−	0.307430i
$199$	180.471	−	104.195i	0.906891	−	0.523594i	0.0274617	−	0.999623i	$-0.491258\pi$
$199$	180.471	−	104.195i	0.906891	−	0.523594i	0.879430	+	0.476029i	$0.157924\pi$
$200$	−202.710	+	14.0502i	−1.01355	+	0.0702508i
$201$	−149.967	+	259.750i	−0.746103	+	1.29229i
$202$	144.380	+	144.380i	0.714752	+	0.714752i
$203$		0			0
$204$			8.65426i			0.0424228i
$205$	−21.1294	+	56.4605i	−0.103070	+	0.275417i
$206$	−79.1994	−	137.177i	−0.384463	−	0.665910i
$207$	−25.8885	+	96.6174i	−0.125065	+	0.466751i
$208$	4.89911	+	18.2837i	0.0235534	+	0.0879026i
$209$			124.112i			0.593839i
$210$		0			0
$211$	−297.303			−1.40902			−0.704509	−	0.709695i	$-0.748833\pi$
$211$	−297.303			−1.40902			−0.704509	+	0.709695i	$0.748833\pi$
$212$	23.2231	−	6.22262i	0.109543	−	0.0293520i
$213$	−516.714	−	138.453i	−2.42589	−	0.650014i
$214$	149.037	−	86.0466i	0.696435	−	0.402087i
$215$	−36.1907	−	79.4776i	−0.168329	−	0.369663i
$216$	−24.1524			−0.111817
$217$		0			0
$218$	118.240	−	118.240i	0.542383	−	0.542383i
$219$	−270.428	−	156.131i	−1.23483	−	0.712929i
$220$	−54.6453	+	45.0180i	−0.248388	+	0.204627i
$221$	−9.55484	−	16.5495i	−0.0432346	−	0.0748845i
$222$	−71.1225	+	19.0572i	−0.320372	+	0.0858433i
$223$	40.6433	−	40.6433i	0.182257	−	0.182257i	−0.610082	−	0.792339i	$-0.708863\pi$
$223$	40.6433	−	40.6433i	0.182257	−	0.182257i	0.792339	+	0.610082i	$0.208863\pi$
$224$		0			0
$225$	−67.3155	−	195.888i	−0.299180	−	0.870613i
$226$	49.4772	−	85.6970i	0.218926	−	0.379190i
$227$	−15.6672	+	58.4709i	−0.0690186	+	0.257581i	−0.991811	−	0.127718i	$-0.959235\pi$
$227$	−15.6672	+	58.4709i	−0.0690186	+	0.257581i	0.922792	+	0.385299i	$0.125902\pi$
$228$	−198.369	−	53.1528i	−0.870040	−	0.233126i
$229$	12.9816	+	7.49491i	0.0566881	+	0.0327289i	0.528076	−	0.849197i	$-0.322914\pi$
$229$	12.9816	+	7.49491i	0.0566881	+	0.0327289i	−0.471388	+	0.881926i	$0.656247\pi$
$230$	−75.9218	+	12.6811i	−0.330095	+	0.0551351i
$231$		0			0
$232$	43.2747	+	43.2747i	0.186529	+	0.186529i
$233$	59.7065	+	222.828i	0.256251	+	0.956341i	0.967390	+	0.253290i	$0.0815128\pi$
$233$	59.7065	+	222.828i	0.256251	+	0.956341i	−0.711139	+	0.703051i	$0.751821\pi$
$234$	−199.405	+	115.127i	−0.852160	+	0.491995i
$235$	21.8646	−	226.346i	0.0930407	−	0.963175i
$236$	25.0498	−	43.3876i	0.106143	−	0.183846i
$237$	−50.4370	−	50.4370i	−0.212814	−	0.212814i
$238$		0			0
$239$			382.834i			1.60182i	0.598786	+	0.800909i	$0.295650\pi$
$239$			382.834i			1.60182i	−0.598786	+	0.800909i	$0.704350\pi$
$240$	7.48223	+	16.4316i	0.0311760	+	0.0684649i
$241$	140.302	+	243.009i	0.582164	+	1.00834i	0.995222	+	0.0976334i	$0.0311273\pi$
$241$	140.302	+	243.009i	0.582164	+	1.00834i	−0.413058	+	0.910705i	$0.635539\pi$
$242$	−28.1922	+	105.215i	−0.116497	+	0.434771i
$243$	−86.6107	−	323.236i	−0.356423	−	1.33019i
$244$			71.7903i			0.294222i
$245$		0			0
$246$	63.9207			0.259840
$247$	438.023	−	117.368i	1.77337	−	0.475174i
$248$	155.492	+	41.6640i	0.626984	+	0.168000i
$249$	−22.5165	+	12.9999i	−0.0904276	+	0.0522084i
$250$	115.722	−	109.615i	0.462889	−	0.438458i
$251$	20.4968			0.0816607			0.0408303	−	0.999166i	$-0.487000\pi$
$251$	20.4968			0.0816607			0.0408303	+	0.999166i	$0.487000\pi$
$252$		0			0
$253$	−50.9196	+	50.9196i	−0.201263	+	0.201263i
$254$	−186.439	−	107.641i	−0.734012	−	0.423782i
$255$	−11.5898	−	14.0684i	−0.0454503	−	0.0551700i
$256$	131.747	+	228.192i	0.514635	+	0.891374i
$257$	−359.460	+	96.3170i	−1.39868	+	0.374774i	−0.877869	−	0.478900i	$-0.841036\pi$
$257$	−359.460	+	96.3170i	−1.39868	+	0.374774i	−0.520807	+	0.853674i	$0.674369\pi$
$258$	−65.4758	+	65.4758i	−0.253782	+	0.253782i
$259$		0			0
$260$	210.556	+	150.285i	0.809829	+	0.578019i
$261$	−31.1925	+	54.0270i	−0.119512	+	0.207000i
$262$	−17.0723	+	63.7147i	−0.0651614	+	0.243186i
$263$	327.017	+	87.6239i	1.24341	+	0.333171i	0.819788	−	0.572668i	$-0.194091\pi$
$263$	327.017	+	87.6239i	1.24341	+	0.333171i	0.423623	+	0.905839i	$0.360758\pi$
$264$	174.558	+	100.781i	0.661204	+	0.381746i
$265$	−29.4182	+	41.2160i	−0.111012	+	0.155532i
$266$		0			0
$267$	−319.638	−	319.638i	−1.19715	−	1.19715i
$268$	−44.3256	−	165.426i	−0.165394	−	0.617260i
$269$	75.2656	−	43.4546i	0.279798	−	0.161541i	−0.353534	−	0.935422i	$-0.615020\pi$
$269$	75.2656	−	43.4546i	0.279798	−	0.161541i	0.633332	+	0.773880i	$0.281687\pi$
$270$	14.6230	−	12.0468i	0.0541594	−	0.0446177i
$271$	99.4914	−	172.324i	0.367127	−	0.635882i	−0.621988	−	0.783027i	$-0.713675\pi$
$271$	99.4914	−	172.324i	0.367127	−	0.635882i	0.989115	+	0.147144i	$0.0470082\pi$
$272$	0.538509	+	0.538509i	0.00197981	+	0.00197981i
$273$		0			0
$274$			249.434i			0.910343i
$275$	28.5430	−	146.363i	0.103793	−	0.532227i
$276$	−59.5779	−	103.192i	−0.215862	−	0.373884i
$277$	−96.5166	+	360.205i	−0.348435	+	1.30038i	0.540112	+	0.841593i	$0.318382\pi$
$277$	−96.5166	+	360.205i	−0.348435	+	1.30038i	−0.888547	+	0.458785i	$0.848285\pi$
$278$	−42.0852	−	157.064i	−0.151386	−	0.564979i
$279$			164.095i			0.588154i
$280$		0			0
$281$	119.086			0.423794			0.211897	−	0.977292i	$-0.432036\pi$
$281$	119.086			0.423794			0.211897	+	0.977292i	$0.432036\pi$
$282$	−232.899	+	62.4052i	−0.825884	+	0.221295i
$283$	−9.42015	−	2.52412i	−0.0332868	−	0.00891916i	0.242137	−	0.970242i	$-0.422152\pi$
$283$	−9.42015	−	2.52412i	−0.0332868	−	0.00891916i	−0.275424	+	0.961323i	$0.588818\pi$
$284$	264.527	−	152.725i	0.931435	−	0.537764i
$285$	393.651	−	179.252i	1.38123	−	0.628953i
$286$	−165.766			−0.579601
$287$		0			0
$288$	−183.981	+	183.981i	−0.638825	+	0.638825i
$289$	249.616	+	144.116i	0.863721	+	0.498670i
$290$	−47.7852	−	4.61596i	−0.164777	−	0.0159171i
$291$	162.960	+	282.255i	0.560000	+	0.969949i
$292$	172.226	−	46.1478i	0.589814	−	0.158040i
$293$	26.5947	−	26.5947i	0.0907669	−	0.0907669i	−0.660265	−	0.751032i	$-0.729556\pi$
$293$	26.5947	−	26.5947i	0.0907669	−	0.0907669i	0.751032	+	0.660265i	$0.229556\pi$
$294$		0			0
$295$	17.3839	+	104.078i	0.0589284	+	0.352806i
$296$	56.4422	−	97.7608i	0.190683	−	0.330273i
$297$	4.58751	−	17.1208i	0.0154462	−	0.0576458i
$298$	−273.123	−	73.1830i	−0.916519	−	0.245581i
$299$	227.861	+	131.555i	0.762076	+	0.439985i
$300$	221.708	+	108.302i	0.739025	+	0.361007i
$301$		0			0
$302$	−59.9391	−	59.9391i	−0.198474	−	0.198474i
$303$	−172.302	−	643.038i	−0.568652	−	2.12224i
$304$	−15.6509	+	9.03604i	−0.0514832	+	0.0297238i
$305$	−96.1419	−	116.702i	−0.315219	−	0.382630i
$306$	−4.63194	+	8.02275i	−0.0151370	+	0.0262181i
$307$	66.6628	+	66.6628i	0.217143	+	0.217143i	0.807293	−	0.590151i	$-0.200932\pi$
$307$	66.6628	+	66.6628i	0.217143	+	0.217143i	−0.590151	+	0.807293i	$0.700932\pi$
$308$		0			0
$309$			516.444i			1.67134i
$310$	−114.924	+	52.3312i	−0.370721	+	0.168810i
$311$	−108.760	−	188.377i	−0.349710	−	0.605715i	0.636488	−	0.771287i	$-0.280386\pi$
$311$	−108.760	−	188.377i	−0.349710	−	0.605715i	−0.986198	+	0.165571i	$0.947053\pi$
$312$	190.609	−	711.362i	0.610926	−	2.28001i
$313$	−47.2552	−	176.359i	−0.150975	−	0.563447i	−0.999416	−	0.0341576i	$-0.989125\pi$
$313$	−47.2552	−	176.359i	−0.150975	−	0.563447i	0.848441	−	0.529290i	$-0.177541\pi$
$314$		−	123.155i		−	0.392213i
$315$		0			0
$316$	40.7285			0.128888
$317$	−478.934	+	128.330i	−1.51083	+	0.404826i	−0.916711	−	0.399550i	$-0.869166\pi$
$317$	−478.934	+	128.330i	−1.51083	+	0.404826i	−0.594120	+	0.804376i	$0.702500\pi$
$318$	51.8625	+	13.8965i	0.163090	+	0.0436997i
$319$	−38.8955	+	22.4564i	−0.121930	+	0.0703961i
$320$	−203.793	−	76.2662i	−0.636853	−	0.238332i
$321$	−561.093			−1.74795
$322$		0			0
$323$	12.9011	−	12.9011i	0.0399413	−	0.0399413i
$324$	178.703	+	103.174i	0.551552	+	0.318439i
$325$	−543.542	+	37.6738i	−1.67244	+	0.115919i
$326$	−27.5692	−	47.7513i	−0.0845682	−	0.146476i
$327$	−526.615	+	141.106i	−1.61044	+	0.431517i
$328$	−69.2943	+	69.2943i	−0.211263	+	0.211263i
$329$		0			0
$330$	−155.953	+	26.0486i	−0.472586	+	0.0789351i
$331$	232.008	−	401.849i	0.700930	−	1.21405i	−0.267210	−	0.963638i	$-0.586102\pi$
$331$	232.008	−	401.849i	0.700930	−	1.21405i	0.968140	−	0.250408i	$-0.0805648\pi$
$332$	3.84238	−	14.3400i	0.0115734	−	0.0431926i
$333$	111.150	+	29.7825i	0.333783	+	0.0894369i
$334$	208.399	+	120.319i	0.623949	+	0.360237i
$335$	293.595	+	209.555i	0.876402	+	0.625536i
$336$		0			0
$337$	−85.3188	−	85.3188i	−0.253171	−	0.253171i	0.569098	−	0.822270i	$-0.307292\pi$
$337$	−85.3188	−	85.3188i	−0.253171	−	0.253171i	−0.822270	+	0.569098i	$0.807292\pi$
$338$	100.982	+	376.869i	0.298762	+	1.11500i
$339$	−279.407	+	161.316i	−0.824209	+	0.475857i
$340$	10.3597	+	1.00072i	0.0304696	+	0.00294330i
$341$	−59.0683	+	102.309i	−0.173221	+	0.300027i
$342$	−155.445	−	155.445i	−0.454519	−	0.454519i
$343$		0			0
$344$		−	141.960i		−	0.412675i
$345$	235.045	+	87.9617i	0.681290	+	0.254962i
$346$	−142.706	−	247.175i	−0.412446	−	0.714378i
$347$	−2.74359	+	10.2392i	−0.00790660	+	0.0295078i	−0.969766	−	0.244035i	$-0.921529\pi$
$347$	−2.74359	+	10.2392i	−0.00790660	+	0.0295078i	0.961860	+	0.273543i	$0.0881955\pi$
$348$	−19.2345	−	71.7840i	−0.0552715	−	0.206276i
$349$		−	32.0826i		−	0.0919272i	−0.998943	−	0.0459636i	$-0.985364\pi$
$349$		−	32.0826i		−	0.0919272i	0.998943	−	0.0459636i	$-0.0146358\pi$
$350$		0			0
$351$	−64.7618			−0.184507
$352$	−180.935	+	48.4813i	−0.514019	+	0.137731i
$353$	484.555	+	129.836i	1.37268	+	0.367807i	0.868455	−	0.495768i	$-0.165113\pi$
$353$	484.555	+	129.836i	1.37268	+	0.367807i	0.504221	+	0.863575i	$0.331780\pi$
$354$	96.8942	−	55.9419i	0.273712	−	0.158028i
$355$	−225.486	+	602.526i	−0.635171	+	1.69726i
$356$	258.112			0.725033
$357$		0			0
$358$	82.1905	−	82.1905i	0.229582	−	0.229582i
$359$	−361.528	−	208.728i	−1.00704	−	0.581415i	−0.0967169	−	0.995312i	$-0.530834\pi$
$359$	−361.528	−	208.728i	−1.00704	−	0.581415i	−0.910324	+	0.413897i	$0.864167\pi$
$360$	32.3745	−	335.147i	0.0899291	−	0.930963i
$361$	35.9763	+	62.3128i	0.0996574	+	0.172612i
$362$	−180.249	+	48.2975i	−0.497924	+	0.133418i
$363$	251.124	−	251.124i	0.691803	−	0.691803i
$364$		0			0
$365$	−218.169	+	305.663i	−0.597723	+	0.837434i
$366$	−80.1619	+	138.844i	−0.219022	+	0.379356i
$367$	86.0920	−	321.300i	0.234583	−	0.875476i	−0.743753	−	0.668454i	$-0.766956\pi$
$367$	86.0920	−	321.300i	0.234583	−	0.875476i	0.978336	−	0.207022i	$-0.0663771\pi$
$368$	−10.1283	−	2.71387i	−0.0275226	−	0.00737465i
$369$	−86.5115	−	49.9475i	−0.234449	−	0.135359i
$370$	14.5885	+	87.3414i	0.0394283	+	0.236058i
$371$		0			0
$372$	−138.224	−	138.224i	−0.371571	−	0.371571i
$373$	108.916	+	406.480i	0.292000	+	1.08976i	0.943571	+	0.331170i	$0.107443\pi$
$373$	108.916	+	406.480i	0.292000	+	1.08976i	−0.651571	+	0.758587i	$0.725890\pi$
$374$	−5.77580	+	3.33466i	−0.0154433	+	0.00891620i
$375$	−505.446	+	120.856i	−1.34786	+	0.322283i
$376$	184.827	−	320.130i	0.491561	−	0.851408i
$377$	116.036	+	116.036i	0.307788	+	0.307788i
$378$		0			0
$379$		−	513.773i		−	1.35560i	−0.735246	−	0.677801i	$-0.762933\pi$
$379$		−	513.773i		−	1.35560i	0.735246	−	0.677801i	$-0.237067\pi$
$380$	−86.5651	+	231.313i	−0.227803	+	0.608719i
$381$	350.952	+	607.866i	0.921133	+	1.59545i
$382$	27.8739	−	104.027i	0.0729684	−	0.272322i
$383$	37.5765	+	140.238i	0.0981111	+	0.366155i	0.997473	−	0.0710499i	$-0.0226350\pi$
$383$	37.5765	+	140.238i	0.0981111	+	0.366155i	−0.899362	+	0.437205i	$0.855968\pi$
$384$		−	291.533i		−	0.759199i
$385$		0			0
$386$	137.494			0.356203
$387$	139.779	−	37.4536i	0.361185	−	0.0967793i
$388$	−179.758	−	48.1661i	−0.463295	−	0.124139i
$389$	−356.579	+	205.871i	−0.916655	+	0.529231i	−0.882566	−	0.470188i	$-0.844186\pi$
$389$	−356.579	+	205.871i	−0.916655	+	0.529231i	−0.0340888	+	0.999419i	$0.510853\pi$
$390$	239.410	+	525.765i	0.613873	+	1.34811i
$391$	10.5858			0.0270737
$392$		0			0
$393$	152.073	−	152.073i	0.386954	−	0.386954i
$394$	76.6629	+	44.2613i	0.194576	+	0.112338i
$395$	−66.2082	+	54.5438i	−0.167616	+	0.138086i
$396$	−58.6602	−	101.602i	−0.148132	−	0.256572i
$397$	−140.406	+	37.6216i	−0.353666	+	0.0947646i	−0.431278	−	0.902219i	$-0.641937\pi$
$397$	−140.406	+	37.6216i	−0.353666	+	0.0947646i	0.0776117	+	0.996984i	$0.475271\pi$
$398$	−187.901	+	187.901i	−0.472113	+	0.472113i
$399$		0			0
$400$	20.5348	−	7.05663i	0.0513369	−	0.0176416i
$401$	26.5072	−	45.9119i	0.0661028	−	0.114493i	−0.831080	−	0.556153i	$-0.812277\pi$
$401$	26.5072	−	45.9119i	0.0661028	−	0.114493i	0.897183	+	0.441660i	$0.145610\pi$
$402$	98.9891	−	369.432i	0.246242	−	0.918986i
$403$	416.933	+	111.717i	1.03457	+	0.277213i
$404$	329.198	+	190.063i	0.814848	+	0.470453i
$405$	−428.671	+	71.6000i	−1.05845	+	0.176790i
$406$		0			0
$407$	58.5786	+	58.5786i	0.143928	+	0.143928i
$408$	−7.66884	−	28.6205i	−0.0187962	−	0.0701483i
$409$	251.839	−	145.399i	0.615742	−	0.355499i	−0.159467	−	0.987203i	$-0.550978\pi$
$409$	251.839	−	145.399i	0.615742	−	0.355499i	0.775209	+	0.631704i	$0.217644\pi$
$410$	7.39137	−	76.5168i	0.0180277	−	0.186626i
$411$	406.628	−	704.300i	0.989362	−	1.71363i
$412$	−208.517	−	208.517i	−0.506110	−	0.506110i
$413$		0			0
$414$		−	127.549i		−	0.308090i
$415$	12.9580	+	28.4568i	0.0312240	+	0.0685705i
$416$	342.205	+	592.716i	0.822608	+	1.42480i
$417$	−137.215	+	512.093i	−0.329053	+	1.22804i
$418$	−40.9617	−	152.871i	−0.0979945	−	0.365721i
$419$		−	290.268i		−	0.692764i	−0.938094	−	0.346382i	$-0.887410\pi$
$419$		−	290.268i		−	0.692764i	0.938094	−	0.346382i	$-0.112590\pi$
$420$		0			0
$421$	256.502			0.609268			0.304634	−	0.952470i	$-0.401466\pi$
$421$	256.502			0.609268			0.304634	+	0.952470i	$0.401466\pi$
$422$	366.193	−	98.1210i	0.867755	−	0.232514i
$423$	363.973	+	97.5264i	0.860457	+	0.230559i
$424$	−71.2871	+	41.1576i	−0.168130	+	0.0970699i
$425$	−18.1808	+	12.2469i	−0.0427784	+	0.0288163i
$426$	682.139			1.60126
$427$		0			0
$428$	226.545	−	226.545i	0.529310	−	0.529310i
$429$	468.055	+	270.232i	1.09104	+	0.629911i
$430$	70.8071	+	85.9495i	0.164668	+	0.199883i
$431$	−145.835	−	252.594i	−0.338364	−	0.586064i	0.645761	−	0.763540i	$-0.276540\pi$
$431$	−145.835	−	252.594i	−0.338364	−	0.586064i	−0.984125	+	0.177475i	$0.943207\pi$
$432$	2.49297	−	0.667990i	0.00577077	−	0.00154627i
$433$	122.368	−	122.368i	0.282605	−	0.282605i	−0.551542	−	0.834147i	$-0.685960\pi$
$433$	122.368	−	122.368i	0.282605	−	0.282605i	0.834147	+	0.551542i	$0.185960\pi$
$434$		0			0
$435$	127.401	+	90.9332i	0.292876	+	0.209042i
$436$	155.652	−	269.596i	0.356999	−	0.618340i
$437$	−65.0162	+	242.644i	−0.148779	+	0.555249i
$438$	384.619	+	103.058i	0.878125	+	0.235293i
$439$	−752.706	−	434.575i	−1.71459	−	0.989921i	−0.928108	−	0.372312i	$-0.878565\pi$
$439$	−752.706	−	434.575i	−1.71459	−	0.989921i	−0.786485	−	0.617609i	$-0.788101\pi$
$440$	140.825	−	197.302i	0.320058	−	0.448414i
$441$		0			0
$442$	17.2308	+	17.2308i	0.0389837	+	0.0389837i
$443$	34.4919	+	128.725i	0.0778597	+	0.290576i	0.993867	−	0.110586i	$-0.0352729\pi$
$443$	34.4919	+	128.725i	0.0778597	+	0.290576i	−0.916007	+	0.401163i	$0.868606\pi$
$444$	−118.713	+	68.5391i	−0.267372	+	0.154367i
$445$	−419.586	+	345.664i	−0.942890	+	0.776774i
$446$	−36.6472	+	63.4748i	−0.0821686	+	0.142320i
$447$	651.884	+	651.884i	1.45835	+	1.45835i
$448$		0			0
$449$		−	758.129i		−	1.68848i	−0.535963	−	0.844242i	$-0.680051\pi$
$449$		−	758.129i		−	1.68848i	0.535963	−	0.844242i	$-0.319949\pi$
$450$	147.564	+	219.062i	0.327920	+	0.486803i
$451$	−35.9586	−	62.2821i	−0.0797307	−	0.138098i
$452$	47.6801	−	177.944i	0.105487	−	0.393682i
$453$	71.5307	+	266.956i	0.157905	+	0.589308i
$454$		−	77.1902i		−	0.170023i
$455$		0			0
$456$	703.127			1.54194
$457$	−705.542	+	189.049i	−1.54386	+	0.413675i	−0.927509	−	0.373800i	$-0.878055\pi$
$457$	−705.542	+	189.049i	−1.54386	+	0.413675i	−0.616347	+	0.787475i	$0.711388\pi$
$458$	−18.4632	−	4.94720i	−0.0403126	−	0.0108017i
$459$	−2.25650	+	1.30279i	−0.00491613	+	0.00283833i
$460$	−130.416	+	59.3858i	−0.283513	+	0.129100i
$461$	−702.980			−1.52490			−0.762452	−	0.647045i	$-0.776004\pi$
$461$	−702.980			−1.52490			−0.762452	+	0.647045i	$0.776004\pi$
$462$		0			0
$463$	618.405	−	618.405i	1.33565	−	1.33565i	0.435420	−	0.900227i	$-0.356600\pi$
$463$	618.405	−	618.405i	1.33565	−	1.33565i	0.900227	−	0.435420i	$-0.143400\pi$
$464$	−5.66360	−	3.26988i	−0.0122060	−	0.00704716i
$465$	409.808	+	39.5866i	0.881307	+	0.0851325i
$466$	−147.083	−	254.755i	−0.315628	−	0.546684i
$467$	120.945	−	32.4072i	0.258983	−	0.0693943i	−0.126991	−	0.991904i	$-0.540532\pi$
$467$	120.945	−	32.4072i	0.258983	−	0.0693943i	0.385974	+	0.922510i	$0.373865\pi$
$468$	−303.108	+	303.108i	−0.647666	+	0.647666i
$469$		0			0
$470$	47.7717	+	286.010i	0.101642	+	0.608532i
$471$	−200.768	+	347.740i	−0.426258	+	0.738301i
$472$	−44.3950	+	165.684i	−0.0940572	+	0.351026i
$473$	100.631	+	26.9639i	0.212750	+	0.0570061i
$474$	78.7701	+	45.4779i	0.166182	+	0.0959450i
$475$	−169.056	−	491.951i	−0.355906	−	1.03569i
$476$		0			0
$477$	−59.3330	−	59.3330i	−0.124388	−	0.124388i
$478$	−126.350	−	471.543i	−0.264330	−	0.986492i
$479$	−644.603	+	372.161i	−1.34573	+	0.776955i	−0.987641	−	0.156734i	$-0.949903\pi$
$479$	−644.603	+	372.161i	−1.34573	+	0.776955i	−0.358085	+	0.933689i	$0.616570\pi$
$480$	415.088	+	503.856i	0.864767	+	1.04970i
$481$	151.343	−	262.134i	0.314642	−	0.544976i
$482$	−253.014	−	253.014i	−0.524925	−	0.524925i
$483$		0			0
$484$			202.786i			0.418980i
$485$	356.719	−	162.435i	0.735504	−	0.334917i
$486$	213.359	+	369.549i	0.439011	+	0.760390i
$487$	173.372	−	647.035i	0.356001	−	1.32861i	−0.523219	−	0.852198i	$-0.675269\pi$
$487$	173.372	−	647.035i	0.356001	−	1.32861i	0.879220	−	0.476416i	$-0.158064\pi$
$488$	−63.6158	−	237.417i	−0.130360	−	0.486511i
$489$			179.774i			0.367635i
$490$		0			0
$491$	−61.5033			−0.125261			−0.0626307	−	0.998037i	$-0.519949\pi$
$491$	−61.5033			−0.125261			−0.0626307	+	0.998037i	$0.519949\pi$
$492$	114.945	−	30.7995i	0.233629	−	0.0626006i
$493$	6.37731	+	1.70880i	0.0129357	+	0.00346612i
$494$	−500.784	+	289.128i	−1.01373	+	0.585279i
$495$	231.424	+	86.6068i	0.467524	+	0.174963i
$496$	−17.2019			−0.0346813
$497$		0			0
$498$	23.4434	−	23.4434i	0.0470752	−	0.0470752i
$499$	−41.8687	−	24.1729i	−0.0839052	−	0.0484427i	0.457460	−	0.889230i	$-0.348759\pi$
$499$	−41.8687	−	24.1729i	−0.0839052	−	0.0484427i	−0.541366	+	0.840787i	$0.682092\pi$
$500$	155.281	−	252.873i	0.310561	−	0.505747i
$501$	−392.289	−	679.465i	−0.783013	−	1.35622i
$502$	−25.2463	+	6.76472i	−0.0502914	+	0.0134755i
$503$	571.523	−	571.523i	1.13623	−	1.13623i	0.147108	−	0.989120i	$-0.453003\pi$
$503$	571.523	−	571.523i	1.13623	−	1.13623i	0.989120	−	0.147108i	$-0.0469965\pi$
$504$		0			0
$505$	−789.678	+	131.898i	−1.56372	+	0.261185i
$506$	45.9131	−	79.5239i	0.0907374	−	0.157162i
$507$	329.241	−	1228.74i	0.649391	−	2.42356i
$508$	−387.129	−	103.731i	−0.762064	−	0.204195i
$509$	579.164	+	334.381i	1.13785	+	0.656936i	0.945897	−	0.324468i	$-0.105185\pi$
$509$	579.164	+	334.381i	1.13785	+	0.656936i	0.191950	+	0.981405i	$0.438519\pi$
$510$	18.9185	+	13.5031i	0.0370950	+	0.0264767i
$511$		0			0
$512$	−39.2534	−	39.2534i	−0.0766668	−	0.0766668i
$513$	−16.0030	−	59.7241i	−0.0311950	−	0.116421i
$514$	410.964	−	237.270i	0.799541	−	0.461615i
$515$	618.214	+	59.7182i	1.20041	+	0.115958i
$516$	−86.1929	+	149.290i	−0.167040	+	0.289323i
$517$	191.823	+	191.823i	0.371030	+	0.371030i
$518$		0			0
$519$			930.561i			1.79299i
$520$	−829.501	−	310.427i	−1.59519	−	0.596975i
$521$	−478.134	−	828.153i	−0.917724	−	1.58954i	−0.802863	−	0.596163i	$-0.796691\pi$
$521$	−478.134	−	828.153i	−0.917724	−	1.58954i	−0.114861	−	0.993382i	$-0.536642\pi$
$522$	20.5894	−	76.8406i	0.0394432	−	0.147204i
$523$	232.525	+	867.796i	0.444599	+	1.65927i	0.716993	+	0.697080i	$0.245518\pi$
$523$	232.525	+	867.796i	0.444599	+	1.65927i	−0.272394	+	0.962186i	$0.587816\pi$
$524$			122.801i			0.234353i
$525$		0			0
$526$	−431.711			−0.820743
$527$	16.7746	−	4.49475i	0.0318304	−	0.00852893i
$528$	−20.8049	−	5.57465i	−0.0394031	−	0.0105580i
$529$	331.904	−	191.625i	0.627417	−	0.362239i
$530$	22.6320	−	60.4755i	0.0427018	−	0.114105i
$531$	−174.851			−0.329287
$532$		0			0
$533$	−185.804	+	185.804i	−0.348601	+	0.348601i
$534$	499.196	+	288.211i	0.934823	+	0.539720i
$535$	−64.8811	+	671.661i	−0.121273	+	1.25544i
$536$	293.179	+	507.800i	0.546975	+	0.947388i
$537$	−366.059	+	98.0853i	−0.681675	+	0.182654i
$538$	−78.3641	+	78.3641i	−0.145658	+	0.145658i
$539$		0			0
$540$	20.4912	−	28.7090i	0.0379467	−	0.0531649i
$541$	−454.145	+	786.602i	−0.839455	+	1.45398i	0.0508961	+	0.998704i	$0.483792\pi$
$541$	−454.145	+	786.602i	−0.839455	+	1.45398i	−0.890351	+	0.455275i	$0.849541\pi$
$542$	−65.6717	+	245.090i	−0.121165	+	0.452196i
$543$	587.683	+	157.469i	1.08229	+	0.289999i
$544$	23.8470	+	13.7681i	0.0438364	+	0.0253089i
$545$	108.018	+	646.705i	0.198198	+	1.18661i
$546$		0			0
$547$	153.413	+	153.413i	0.280462	+	0.280462i	0.833293	−	0.552831i	$-0.186453\pi$
$547$	153.413	+	153.413i	0.280462	+	0.280462i	−0.552831	+	0.833293i	$0.686453\pi$
$548$	120.187	+	448.544i	0.219319	+	0.818511i
$549$	216.985	−	125.277i	0.395237	−	0.228190i
$550$	13.1482	+	189.697i	0.0239059	+	0.344904i
$551$	−78.3365	+	135.683i	−0.142172	+	0.246248i
$552$	288.472	+	288.472i	0.522594	+	0.522594i
$553$		0			0
$554$		−	475.524i		−	0.858346i
$555$	101.192	−	270.399i	0.182328	−	0.487205i
$556$	−151.359	−	262.162i	−0.272229	−	0.471514i
$557$	110.673	−	413.039i	0.198696	−	0.741542i	−0.792584	−	0.609763i	$-0.791265\pi$
$557$	110.673	−	413.039i	0.198696	−	0.741542i	0.991279	−	0.131779i	$-0.0420688\pi$
$558$	−54.1575	−	202.118i	−0.0970564	−	0.362219i
$559$		−	380.649i		−	0.680946i
$560$		0			0
$561$	21.7447			0.0387606
$562$	−146.680	+	39.3028i	−0.260997	+	0.0699338i
$563$	178.196	+	47.7474i	0.316511	+	0.0848088i	0.413577	−	0.910469i	$-0.364279\pi$
$563$	178.196	+	47.7474i	0.316511	+	0.0848088i	−0.0970662	+	0.995278i	$0.530946\pi$
$564$	−388.741	+	224.440i	−0.689257	+	0.397943i
$565$	160.795	+	353.120i	0.284594	+	0.624990i
$566$	12.4360			0.0219717
$567$		0			0
$568$	−739.484	+	739.484i	−1.30191	+	1.30191i
$569$	−211.620	−	122.179i	−0.371916	−	0.214726i	0.302379	−	0.953188i	$-0.402219\pi$
$569$	−211.620	−	122.179i	−0.371916	−	0.214726i	−0.674295	+	0.738462i	$0.735552\pi$
$570$	−425.707	+	350.707i	−0.746854	+	0.615275i
$571$	−89.0175	−	154.183i	−0.155897	−	0.270022i	0.777488	−	0.628898i	$-0.216494\pi$
$571$	−89.0175	−	154.183i	−0.155897	−	0.270022i	−0.933385	+	0.358875i	$0.883160\pi$
$572$	−298.088	+	79.8724i	−0.521133	+	0.139637i
$573$	−248.290	+	248.290i	−0.433315	+	0.433315i
$574$		0			0
$575$	132.474	−	271.191i	0.230390	−	0.471637i
$576$	180.284	−	312.261i	0.312993	−	0.542120i
$577$	−131.070	+	489.160i	−0.227158	+	0.847765i	0.754370	+	0.656449i	$0.227942\pi$
$577$	−131.070	+	489.160i	−0.227158	+	0.847765i	−0.981528	+	0.191316i	$0.938724\pi$
$578$	−355.019	−	95.1270i	−0.614219	−	0.164580i
$579$	−388.228	−	224.144i	−0.670515	−	0.387122i
$580$	−88.1538	+	14.7242i	−0.151989	+	0.0253865i
$581$		0			0
$582$	−293.875	−	293.875i	−0.504940	−	0.504940i
$583$	−15.6349	−	58.3504i	−0.0268181	−	0.100086i
$584$	−528.674	+	305.230i	−0.905264	+	0.522655i
$585$	86.8082	−	898.655i	0.148390	−	1.53616i
$586$	−23.9799	+	41.5343i	−0.0409213	+	0.0708777i
$587$	−178.183	−	178.183i	−0.303548	−	0.303548i	0.538852	−	0.842400i	$-0.318858\pi$
$587$	−178.183	−	178.183i	−0.303548	−	0.303548i	−0.842400	+	0.538852i	$0.818858\pi$
$588$		0			0
$589$			412.107i			0.699671i
$590$	−55.7615	−	122.457i	−0.0945110	−	0.207554i
$591$	−144.310	−	249.952i	−0.244179	−	0.422931i
$592$	−3.12207	+	11.6517i	−0.00527377	+	0.0196820i
$593$	−235.528	−	879.002i	−0.397180	−	1.48230i	−0.818034	−	0.575169i	$-0.804936\pi$
$593$	−235.528	−	879.002i	−0.397180	−	1.48230i	0.420854	−	0.907128i	$-0.361730\pi$
$594$			22.6020i			0.0380505i
$595$		0			0
$596$	−526.405			−0.883229
$597$	836.873	−	224.239i	1.40180	−	0.375610i
$598$	−324.078	−	86.8363i	−0.541936	−	0.145211i
$599$	−3.19934	+	1.84714i	−0.00534113	+	0.00308371i	−0.502668	−	0.864479i	$-0.667648\pi$
$599$	−3.19934	+	1.84714i	−0.00534113	+	0.00308371i	0.497327	+	0.867563i	$0.334315\pi$
$600$	−829.179	−	161.703i	−1.38196	−	0.269505i
$601$	−77.7927			−0.129439			−0.0647194	−	0.997904i	$-0.520615\pi$
$601$	−77.7927			−0.129439			−0.0647194	+	0.997904i	$0.520615\pi$
$602$		0			0
$603$	−422.647	+	422.647i	−0.700907	+	0.700907i
$604$	−136.666	−	78.9043i	−0.226269	−	0.130636i
$605$	−271.572	−	329.649i	−0.448880	−	0.544874i
$606$	424.453	+	735.174i	0.700418	+	1.21316i
$607$	663.561	−	177.801i	1.09318	−	0.292917i	0.333197	−	0.942857i	$-0.391873\pi$
$607$	663.561	−	177.801i	1.09318	−	0.292917i	0.759985	+	0.649940i	$0.225206\pi$
$608$	−462.049	+	462.049i	−0.759949	+	0.759949i
$609$		0			0
$610$	156.936	+	112.013i	0.257271	+	0.183629i
$611$	495.591	−	858.388i	0.811114	−	1.40489i
$612$	−4.46369	+	16.6587i	−0.00729362	+	0.0272202i
$613$	−255.220	−	68.3861i	−0.416346	−	0.111560i	0.0445637	−	0.999007i	$-0.485810\pi$
$613$	−255.220	−	68.3861i	−0.416346	−	0.111560i	−0.460910	+	0.887447i	$0.652477\pi$
$614$	−104.111	−	60.1084i	−0.169561	−	0.0978964i
$615$	−145.608	+	204.003i	−0.236761	+	0.331712i
$616$		0			0
$617$	285.496	+	285.496i	0.462717	+	0.462717i	0.899545	−	0.436828i	$-0.143898\pi$
$617$	285.496	+	285.496i	0.462717	+	0.462717i	−0.436828	+	0.899545i	$0.643898\pi$
$618$	−170.446	−	636.112i	−0.275802	−	1.02931i
$619$	296.838	−	171.380i	0.479545	−	0.276866i	−0.240682	−	0.970604i	$-0.577371\pi$
$619$	296.838	−	171.380i	0.479545	−	0.276866i	0.720227	+	0.693739i	$0.244038\pi$
$620$	−181.446	+	149.479i	−0.292655	+	0.241095i
$621$	17.9375	−	31.0686i	0.0288848	−	0.0500299i
$622$	196.133	+	196.133i	0.315326	+	0.315326i
$623$		0			0
$624$			78.6972i			0.126117i
$625$	86.2254	+	619.024i	0.137961	+	0.990438i
$626$	116.410	+	201.628i	0.185959	+	0.322090i
$627$	−133.552	+	498.422i	−0.213001	+	0.794931i
$628$	−59.3409	−	221.463i	−0.0944918	−	0.352648i
$629$		−	12.1781i		−	0.0193610i
$630$		0			0
$631$	651.848			1.03304			0.516520	−	0.856275i	$-0.327227\pi$
$631$	651.848			1.03304			0.516520	+	0.856275i	$0.327227\pi$
$632$	−134.693	+	36.0909i	−0.213122	+	0.0571059i
$633$	−1193.94	−	319.914i	−1.88615	−	0.505394i
$634$	547.556	−	316.132i	0.863653	−	0.498630i
$635$	768.233	−	349.820i	1.20982	−	0.550898i
$636$	99.9574			0.157166
$637$		0			0
$638$	40.4968	−	40.4968i	0.0634746	−	0.0634746i
$639$	−923.219	−	533.021i	−1.44479	−	0.834149i
$640$	−348.981	−	33.7109i	−0.545283	−	0.0526733i
$641$	222.071	+	384.639i	0.346445	+	0.600061i	0.985615	−	0.169005i	$-0.0540553\pi$
$641$	222.071	+	384.639i	0.346445	+	0.600061i	−0.639170	+	0.769065i	$0.720722\pi$
$642$	691.107	−	185.182i	1.07649	−	0.288445i
$643$	251.202	−	251.202i	0.390672	−	0.390672i	−0.484255	−	0.874927i	$-0.660909\pi$
$643$	251.202	−	251.202i	0.390672	−	0.390672i	0.874927	+	0.484255i	$0.160909\pi$
$644$		0			0
$645$	−59.8155	−	358.116i	−0.0927371	−	0.555219i
$646$	−11.6326	+	20.1482i	−0.0180071	+	0.0311892i
$647$	−64.2707	+	239.862i	−0.0993365	+	0.370729i	−0.997641	−	0.0686441i	$-0.978133\pi$
$647$	−64.2707	+	239.862i	−0.0993365	+	0.370729i	0.898305	+	0.439373i	$0.144799\pi$
$648$	−682.414	−	182.852i	−1.05311	−	0.282179i
$649$	−109.016	−	62.9401i	−0.167975	−	0.0969802i
$650$	657.055	−	225.792i	1.01085	−	0.347373i
$651$		0			0
$652$	−72.5847	−	72.5847i	−0.111326	−	0.111326i
$653$	−195.601	−	729.993i	−0.299542	−	1.11791i	−0.937543	−	0.347870i	$-0.886905\pi$
$653$	−195.601	−	729.993i	−0.299542	−	1.11791i	0.638000	−	0.770036i	$-0.279762\pi$
$654$	602.069	−	347.605i	0.920595	−	0.531506i
$655$	−164.456	−	199.625i	−0.251077	−	0.304771i
$656$	5.23595	−	9.06892i	0.00798162	−	0.0138246i
$657$	−440.021	−	440.021i	−0.669743	−	0.669743i
$658$		0			0
$659$			587.795i			0.891950i	0.895045	+	0.445975i	$0.147143\pi$
$659$			587.795i			0.891950i	−0.895045	+	0.445975i	$0.852857\pi$
$660$	−267.891	+	121.986i	−0.405896	+	0.184827i
$661$	87.0160	+	150.716i	0.131643	+	0.228012i	0.924310	−	0.381642i	$-0.124641\pi$
$661$	87.0160	+	150.716i	0.131643	+	0.228012i	−0.792667	+	0.609655i	$0.791308\pi$
$662$	−153.142	+	571.535i	−0.231333	+	0.863346i
$663$	−20.5630	−	76.7423i	−0.0310152	−	0.115750i
$664$			50.8285i			0.0765489i
$665$		0			0
$666$	−146.734			−0.220322
$667$	−87.8058	+	23.5275i	−0.131643	+	0.0352736i
$668$	432.728	+	115.949i	0.647796	+	0.173576i
$669$	206.954	−	119.485i	0.309348	−	0.178602i
$670$	−430.786	−	161.214i	−0.642964	−	0.240619i
$671$	180.380			0.268823
$672$		0			0
$673$	280.346	−	280.346i	0.416562	−	0.416562i	−0.467455	−	0.884017i	$-0.654829\pi$
$673$	280.346	−	280.346i	0.416562	−	0.416562i	0.884017	+	0.467455i	$0.154829\pi$
$674$	133.247	+	76.9301i	0.197696	+	0.114140i
$675$	5.13679	+	74.1114i	0.00761006	+	0.109795i
$676$	363.180	+	629.046i	0.537249	+	0.930542i
$677$	334.663	−	89.6728i	0.494333	−	0.132456i	−0.00303575	−	0.999995i	$-0.500966\pi$
$677$	334.663	−	89.6728i	0.494333	−	0.132456i	0.497369	+	0.867539i	$0.334300\pi$
$678$	290.910	−	290.910i	0.429070	−	0.429070i
$679$		0			0
$680$	−35.1472	+	5.87056i	−0.0516870	+	0.00863318i
$681$	−125.836	+	217.954i	−0.184781	+	0.320050i
$682$	38.9895	−	145.511i	0.0571693	−	0.213359i
$683$	−391.865	−	105.000i	−0.573741	−	0.153733i	−0.0397293	−	0.999210i	$-0.512650\pi$
$683$	−391.865	−	105.000i	−0.573741	−	0.153733i	−0.534012	+	0.845477i	$0.679316\pi$
$684$	−354.429	−	204.630i	−0.518171	−	0.299166i
$685$	−796.068	−	568.198i	−1.16214	−	0.829486i
$686$		0			0
$687$	44.0676	+	44.0676i	0.0641450	+	0.0641450i
$688$	3.92623	+	14.6529i	0.00570673	+	0.0212978i
$689$	−191.148	+	110.359i	−0.277428	+	0.160173i
$690$	−318.539	−	30.7702i	−0.461651	−	0.0445945i
$691$	−207.562	+	359.508i	−0.300380	+	0.520273i	−0.976222	−	0.216773i	$-0.930447\pi$
$691$	−207.562	+	359.508i	−0.300380	+	0.520273i	0.675842	+	0.737046i	$0.263780\pi$
$692$	−375.720	−	375.720i	−0.542948	−	0.542948i
$693$		0			0
$694$		−	13.5173i		−	0.0194774i
$695$	597.138	+	223.469i	0.859192	+	0.321538i
$696$	127.221	+	220.353i	0.182788	+	0.316599i
$697$	−2.73623	+	10.2118i	−0.00392573	+	0.0146510i
$698$	10.5884	+	39.5166i	0.0151697	+	0.0566140i
$699$			959.098i			1.37210i
$700$		0			0
$701$	−13.0606			−0.0186314			−0.00931568	−	0.999957i	$-0.502965\pi$
$701$	−13.0606			−0.0186314			−0.00931568	+	0.999957i	$0.502965\pi$
$702$	79.7681	−	21.3738i	0.113630	−	0.0304470i
$703$	279.140	+	74.7954i	0.397070	+	0.106395i
$704$	224.806	−	129.792i	0.319326	−	0.184363i
$705$	331.366	−	885.453i	0.470023	−	1.25596i
$706$	−639.684			−0.906068
$707$		0			0
$708$	147.285	−	147.285i	0.208029	−	0.208029i
$709$	−201.983	−	116.615i	−0.284885	−	0.164478i	0.350748	−	0.936470i	$-0.385927\pi$
$709$	−201.983	−	116.615i	−0.284885	−	0.164478i	−0.635633	+	0.771992i	$0.719261\pi$
$710$	78.8780	−	816.559i	0.111096	−	1.15008i
$711$	−71.0726	−	123.101i	−0.0999615	−	0.173138i
$712$	−853.601	+	228.722i	−1.19888	+	0.321238i
$713$	−169.075	+	169.075i	−0.237132	+	0.237132i
$714$		0			0
$715$	377.606	−	529.042i	0.528120	−	0.739918i
$716$	108.196	−	187.401i	0.151112	−	0.261734i
$717$	−411.951	+	1537.42i	−0.574548	+	2.14424i
$718$	514.187	+	137.776i	0.716138	+	0.191889i
$719$	−154.548	−	89.2281i	−0.214948	−	0.124100i	0.388661	−	0.921381i	$-0.372938\pi$
$719$	−154.548	−	89.2281i	−0.214948	−	0.124100i	−0.603609	+	0.797281i	$0.706271\pi$
$720$	5.92759	+	35.4886i	0.00823277	+	0.0492897i
$721$		0			0
$722$	−64.8781	−	64.8781i	−0.0898589	−	0.0898589i
$723$	301.944	+	1126.87i	0.417627	+	1.55860i
$724$	−300.860	+	173.701i	−0.415552	+	0.239919i
$725$	123.584	−	141.992i	0.170461	−	0.195851i
$726$	−226.433	+	392.194i	−0.311892	+	0.540212i
$727$	−536.560	−	536.560i	−0.738047	−	0.738047i	0.234153	−	0.972200i	$-0.424768\pi$
$727$	−536.560	−	536.560i	−0.738047	−	0.738047i	−0.972200	+	0.234153i	$0.924768\pi$
$728$		0			0
$729$		−	608.980i		−	0.835363i
$730$	167.842	−	448.494i	0.229920	−	0.614376i
$731$	−7.65740	−	13.2630i	−0.0104752	−	0.0181436i
$732$	−77.2502	+	288.302i	−0.105533	+	0.393855i
$733$	68.3024	+	254.908i	0.0931820	+	0.347760i	0.996738	−	0.0807110i	$-0.0257191\pi$
$733$	68.3024	+	254.908i	0.0931820	+	0.347760i	−0.903556	+	0.428471i	$0.859052\pi$
$734$			424.163i			0.577879i
$735$		0			0
$736$	−379.130			−0.515122
$737$	−415.648	+	111.373i	−0.563973	+	0.151116i
$738$	123.042	+	32.9690i	0.166724	+	0.0446735i
$739$	262.146	−	151.350i	0.354730	−	0.204804i	−0.312037	−	0.950070i	$-0.601011\pi$
$739$	262.146	−	151.350i	0.354730	−	0.204804i	0.666767	+	0.745267i	$0.267678\pi$
$740$	68.3181	+	150.032i	0.0923218	+	0.202746i
$741$	1885.35			2.54433
$742$		0			0
$743$	−767.699	+	767.699i	−1.03324	+	1.03324i	−0.0338136	+	0.999428i	$0.510765\pi$
$743$	−767.699	+	767.699i	−1.03324	+	1.03324i	−0.999428	+	0.0338136i	$0.989235\pi$
$744$	579.607	+	334.636i	0.779041	+	0.449780i
$745$	855.723	−	704.964i	1.14862	−	0.946260i
$746$	−268.307	−	464.721i	−0.359660	−	0.622950i
$747$	−50.0474	+	13.4102i	−0.0669979	+	0.0179520i
$748$	−8.77955	+	8.77955i	−0.0117374	+	0.0117374i
$749$		0			0
$750$	582.679	−	315.676i	0.776905	−	0.420902i
$751$	−519.734	+	900.206i	−0.692056	+	1.19868i	0.279107	+	0.960260i	$0.409962\pi$
$751$	−519.734	+	900.206i	−0.692056	+	1.19868i	−0.971163	+	0.238416i	$0.923372\pi$
$752$	−10.2236	+	38.1550i	−0.0135952	+	0.0507380i
$753$	82.3130	+	22.0557i	0.109313	+	0.0292904i
$754$	−181.219	−	104.627i	−0.240344	−	0.138763i
$755$	327.834	−	54.7574i	0.434217	−	0.0725263i
$756$		0			0
$757$	612.294	+	612.294i	0.808843	+	0.808843i	0.984459	−	0.175616i	$-0.0561916\pi$
$757$	612.294	+	612.294i	0.808843	+	0.808843i	−0.175616	+	0.984459i	$0.556192\pi$
$758$	169.564	+	632.822i	0.223699	+	0.834857i
$759$	−259.280	+	149.695i	−0.341607	+	0.197227i
$760$	81.3049	−	841.683i	0.106980	−	1.10748i
$761$	−340.196	+	589.237i	−0.447038	+	0.774293i	−0.998192	−	0.0601112i	$-0.980854\pi$
$761$	−340.196	+	589.237i	−0.447038	+	0.774293i	0.551154	+	0.834404i	$0.314188\pi$
$762$	−632.891	−	632.891i	−0.830566	−	0.830566i
$763$		0			0
$764$		−	200.497i		−	0.262430i
$765$	−15.0533	−	33.0582i	−0.0196775	−	0.0432134i
$766$	−92.5672	−	160.331i	−0.120845	−	0.209310i
$767$	−119.040	+	444.263i	−0.155202	+	0.579221i
$768$	283.533	+	1058.16i	0.369183	+	1.37781i
$769$			1288.89i			1.67606i	0.545627	+	0.838028i	$0.316292\pi$
$769$			1288.89i			1.67606i	−0.545627	+	0.838028i	$0.683708\pi$
$770$		0			0
$771$	−1547.19			−2.00674
$772$	247.249	−	66.2502i	0.320271	−	0.0858163i
$773$	303.870	+	81.4217i	0.393105	+	0.105332i	0.449956	−	0.893051i	$-0.351440\pi$
$773$	303.870	+	81.4217i	0.393105	+	0.105332i	−0.0568517	+	0.998383i	$0.518106\pi$
$774$	−159.807	+	92.2644i	−0.206468	+	0.119205i
$775$	94.7749	−	485.986i	0.122290	−	0.627079i
$776$	637.160			0.821083
$777$		0			0
$778$	371.259	−	371.259i	0.477196	−	0.477196i
$779$	−217.264	−	125.437i	−0.278901	−	0.161024i
$780$	683.853	+	830.097i	0.876735	+	1.06423i
$781$	−383.737	−	664.651i	−0.491340	−	0.851026i
$782$	−13.0387	+	3.49372i	−0.0166736	+	0.00446767i
$783$	15.8214	−	15.8214i	0.0202061	−	0.0202061i
$784$		0			0
$785$	393.049	+	280.541i	0.500699	+	0.357377i
$786$	−137.121	+	237.500i	−0.174454	+	0.302163i
$787$	358.940	−	1339.58i	0.456086	−	1.70214i	−0.228789	−	0.973476i	$-0.573477\pi$
$787$	358.940	−	1339.58i	0.456086	−	1.70214i	0.684875	−	0.728660i	$-0.259857\pi$
$788$	159.186	+	42.6537i	0.202012	+	0.0541290i
$789$	1218.98	+	703.776i	1.54496	+	0.891985i
$790$	63.5482	−	89.0336i	0.0804407	−	0.112701i
$791$		0			0
$792$	284.028	+	284.028i	0.358622	+	0.358622i
$793$	−170.578	−	636.606i	−0.215105	−	0.802782i
$794$	160.523	−	92.6781i	0.202170	−	0.116723i
$795$	−162.491	+	133.864i	−0.204391	+	0.168382i
$796$	−247.354	+	428.431i	−0.310747	+	0.538229i
$797$	905.526	+	905.526i	1.13617	+	1.13617i	0.989131	+	0.147038i	$0.0469738\pi$
$797$	905.526	+	905.526i	1.13617	+	1.13617i	0.147038	+	0.989131i	$0.453026\pi$
$798$		0			0
$799$		−	39.8786i		−	0.0499106i
$800$	651.143	−	438.622i	0.813929	−	0.548277i
$801$	−450.414	−	780.140i	−0.562314	−	0.973957i
$802$	−17.4967	+	65.2987i	−0.0218164	+	0.0814198i
$803$	−115.951	−	432.734i	−0.144397	−	0.538897i
$804$		−	712.028i		−	0.885606i
$805$		0			0
$806$	−550.414			−0.682895
$807$	349.018	−	93.5190i	0.432488	−	0.115885i
$808$	−1257.11	−	336.842i	−1.55583	−	0.416884i
$809$	−313.879	+	181.218i	−0.387983	+	0.224002i	−0.681286	−	0.732017i	$-0.738579\pi$
$809$	−313.879	+	181.218i	−0.387983	+	0.224002i	0.293303	+	0.956020i	$0.405246\pi$
$810$	504.369	−	229.668i	0.622678	−	0.283541i
$811$	−668.488			−0.824276			−0.412138	−	0.911121i	$-0.635218\pi$
$811$	−668.488			−0.824276			−0.412138	+	0.911121i	$0.635218\pi$
$812$		0			0
$813$	584.976	−	584.976i	0.719528	−	0.719528i
$814$	−91.4852	−	52.8190i	−0.112390	−	0.0648882i
$815$	215.199	+	20.7878i	0.264048	+	0.0255065i
$816$	1.58313	+	2.74206i	0.00194011	+	0.00336036i
$817$	351.039	−	94.0606i	0.429668	−	0.115129i
$818$	−262.206	+	262.206i	−0.320546	+	0.320546i
$819$		0			0
$820$	−23.5773	−	141.158i	−0.0287528	−	0.172143i
$821$	360.015	−	623.564i	0.438508	−	0.759518i	−0.559067	−	0.829123i	$-0.688840\pi$
$821$	360.015	−	623.564i	0.438508	−	0.759518i	0.997575	+	0.0696047i	$0.0221738\pi$
$822$	−268.405	+	1001.70i	−0.326526	+	1.21861i
$823$	−706.861	−	189.403i	−0.858884	−	0.230137i	−0.197609	−	0.980281i	$-0.563318\pi$
$823$	−706.861	−	189.403i	−0.858884	−	0.230137i	−0.661275	+	0.750144i	$0.729984\pi$
$824$	874.362	+	504.813i	1.06112	+	0.612637i
$825$	272.120	−	557.062i	0.329842	−	0.675227i
$826$		0			0
$827$	−709.579	−	709.579i	−0.858016	−	0.858016i	0.133088	−	0.991104i	$-0.457511\pi$
$827$	−709.579	−	709.579i	−0.858016	−	0.858016i	−0.991104	+	0.133088i	$0.957511\pi$
$828$	−61.4582	−	229.365i	−0.0742249	−	0.277011i
$829$	1403.34	−	810.220i	1.69281	−	0.977346i	0.740582	−	0.671966i	$-0.234550\pi$
$829$	1403.34	−	810.220i	1.69281	−	0.977346i	0.952231	−	0.305379i	$-0.0987832\pi$
$830$	−25.3523	−	30.7740i	−0.0305450	−	0.0370771i
$831$	−775.200	+	1342.69i	−0.932852	+	1.61575i
$832$	−670.656	−	670.656i	−0.806077	−	0.806077i
$833$		0			0
$834$		−	676.039i		−	0.810598i
$835$	−858.721	+	391.024i	−1.02841	+	0.468293i
$836$	−147.319	−	255.163i	−0.176218	−	0.305219i
$837$	15.2325	−	56.8484i	0.0181989	−	0.0679193i
$838$	95.7992	+	357.527i	0.114319	+	0.426644i
$839$		−	451.819i		−	0.538521i	−0.963067	−	0.269260i	$-0.913221\pi$
$839$		−	451.819i		−	0.538521i	0.963067	−	0.269260i	$-0.0867793\pi$
$840$		0			0
$841$	784.305			0.932586
$842$	−315.937	+	84.6551i	−0.375222	+	0.100540i
$843$	478.236	+	128.143i	0.567303	+	0.152008i
$844$	611.226	−	352.892i	0.724202	−	0.418118i
$845$	−1432.81	−	536.205i	−1.69563	−	0.634562i
$846$	−480.499			−0.567966
$847$		0			0
$848$	6.21982	−	6.21982i	0.00733470	−	0.00733470i
$849$	−35.1142	−	20.2732i	−0.0413595	−	0.0238789i
$850$	18.3516	−	21.0851i	0.0215902	−	0.0248060i
$851$	83.8366	+	145.209i	0.0985154	+	0.170634i
$852$	1226.65	−	328.681i	1.43973	−	0.385776i
$853$	466.163	−	466.163i	0.546499	−	0.546499i	−0.378928	−	0.925426i	$-0.623707\pi$
$853$	466.163	−	466.163i	0.546499	−	0.546499i	0.925426	+	0.378928i	$0.123707\pi$
$854$		0			0
$855$	850.200	−	142.007i	0.994386	−	0.166090i
$856$	−548.457	+	949.955i	−0.640721	+	1.10976i
$857$	−40.3902	+	150.738i	−0.0471298	+	0.175891i	−0.985479	−	0.169799i	$-0.945688\pi$
$857$	−40.3902	+	150.738i	−0.0471298	+	0.175891i	0.938349	+	0.345689i	$0.112355\pi$
$858$	−665.697	−	178.373i	−0.775871	−	0.207894i
$859$	14.0348	+	8.10300i	0.0163386	+	0.00943307i	0.508147	−	0.861270i	$-0.330331\pi$
$859$	14.0348	+	8.10300i	0.0163386	+	0.00943307i	−0.491808	+	0.870703i	$0.663664\pi$
$860$	168.743	+	120.441i	0.196212	+	0.140047i
$861$		0			0
$862$	262.993	+	262.993i	0.305096	+	0.305096i
$863$	422.849	+	1578.10i	0.489976	+	1.82862i	0.556523	+	0.830832i	$0.312135\pi$
$863$	422.849	+	1578.10i	0.489976	+	1.82862i	−0.0665465	+	0.997783i	$0.521198\pi$
$864$	80.8163	−	46.6593i	0.0935374	−	0.0540038i
$865$	1113.94	+	107.604i	1.28779	+	0.124398i
$866$	−110.337	+	191.109i	−0.127409	+	0.220680i
$867$	847.352	+	847.352i	0.977338	+	0.977338i
$868$		0			0
$869$		−	102.334i		−	0.117761i
$870$	−186.933	−	69.9567i	−0.214866	−	0.0804100i
$871$	786.122	+	1361.60i	0.902552	+	1.56327i
$872$	−275.856	+	1029.51i	−0.316349	+	1.18063i
$873$	168.103	+	627.369i	0.192558	+	0.718636i
$874$		−	320.326i		−	0.366506i
$875$		0			0
$876$	741.297			0.846230
$877$	662.129	−	177.417i	0.754993	−	0.202300i	0.139261	−	0.990256i	$-0.455527\pi$
$877$	662.129	−	177.417i	0.754993	−	0.202300i	0.615732	+	0.787956i	$0.288861\pi$
$878$	1070.55	+	286.852i	1.21930	+	0.326711i
$879$	135.419	−	78.1840i	0.154060	−	0.0889466i
$880$	−9.07891	+	24.2600i	−0.0103169	+	0.0275682i
$881$	974.437			1.10606			0.553029	−	0.833162i	$-0.313472\pi$
$881$	974.437			1.10606			0.553029	+	0.833162i	$0.313472\pi$
$882$		0			0
$883$	191.886	−	191.886i	0.217311	−	0.217311i	−0.590053	−	0.807365i	$-0.700893\pi$
$883$	191.886	−	191.886i	0.217311	−	0.217311i	0.807365	+	0.590053i	$0.200893\pi$
$884$	39.2876	+	22.6827i	0.0444430	+	0.0256592i
$885$	−42.1815	+	436.670i	−0.0476627	+	0.493413i
$886$	−84.9683	−	147.169i	−0.0959010	−	0.166105i
$887$	948.556	−	254.165i	1.06940	−	0.286544i	0.319152	−	0.947703i	$-0.396602\pi$
$887$	948.556	−	254.165i	1.06940	−	0.286544i	0.750246	+	0.661159i	$0.229935\pi$
$888$	331.862	−	331.862i	0.373718	−	0.373718i
$889$		0			0
$890$	402.729	−	564.239i	0.452504	−	0.633977i
$891$	259.235	−	449.008i	0.290949	−	0.503938i
$892$	−35.3161	+	131.801i	−0.0395920	+	0.147759i
$893$	914.079	+	244.927i	1.02360	+	0.274274i
$894$	−1018.08	−	587.790i	−1.13879	−	0.657483i
$895$	75.0852	+	449.536i	0.0838940	+	0.502275i
$896$		0			0
$897$	773.502	+	773.502i	0.862321	+	0.862321i
$898$	250.211	+	933.799i	0.278631	+	1.03987i
$899$	−129.150	+	74.5647i	−0.143659	+	0.0829418i
$900$	370.909	+	322.825i	0.412121	+	0.358694i
$901$	−4.44012	+	7.69052i	−0.00492799	+	0.00853554i
$902$	64.8461	+	64.8461i	0.0718915	+	0.0718915i
$903$		0			0
$904$			630.730i			0.697711i
$905$	256.456	−	685.282i	0.283376	−	0.757218i
$906$	−176.211	−	305.206i	−0.194493	−	0.336872i
$907$	231.530	−	864.080i	0.255270	−	0.952680i	−0.712670	−	0.701499i	$-0.752515\pi$
$907$	231.530	−	864.080i	0.255270	−	0.952680i	0.967940	−	0.251181i	$-0.0808188\pi$
$908$	−37.1932	−	138.807i	−0.0409617	−	0.152871i
$909$		−	1326.67i		−	1.45948i
$910$		0			0
$911$	670.054			0.735515			0.367757	−	0.929922i	$-0.380126\pi$
$911$	670.054			0.735515			0.367757	+	0.929922i	$0.380126\pi$
$912$	−72.5755	+	19.4465i	−0.0795784	+	0.0213230i
$913$	−36.0305	−	9.65436i	−0.0394639	−	0.0105743i
$914$	806.634	−	465.710i	0.882532	−	0.509530i
$915$	−260.517	−	572.117i	−0.284718	−	0.625265i
$916$	−35.5851			−0.0388484
$917$		0			0
$918$	2.34940	−	2.34940i	0.00255926	−	0.00255926i
$919$	−224.983	−	129.894i	−0.244813	−	0.141343i	0.372574	−	0.928003i	$-0.378475\pi$
$919$	−224.983	−	129.894i	−0.244813	−	0.141343i	−0.617387	+	0.786660i	$0.711809\pi$
$920$	378.675	−	311.961i	0.411603	−	0.339088i
$921$	195.978	+	339.443i	0.212788	+	0.368559i
$922$	865.872	−	232.010i	0.939123	−	0.251637i
$923$	−1982.83	+	1982.83i	−2.14825	+	2.14825i
$924$		0			0
$925$	−311.982	−	152.400i	−0.337277	−	0.164757i
$926$	−557.602	+	965.795i	−0.602162	+	1.04298i
$927$	−266.372	+	994.112i	−0.287348	+	1.07240i
$928$	−228.402	−	61.2003i	−0.246123	−	0.0659486i
$929$	−1154.31	−	666.442i	−1.24253	−	0.717376i	−0.272922	−	0.962036i	$-0.587990\pi$
$929$	−1154.31	−	666.442i	−1.24253	−	0.717376i	−0.969609	+	0.244660i	$0.921324\pi$
$930$	−517.832	+	86.4924i	−0.556808	+	0.0930026i
$931$		0			0
$932$	−387.242	−	387.242i	−0.415495	−	0.415495i
$933$	−234.063	−	873.534i	−0.250871	−	0.936264i
$934$	−138.274	+	79.8328i	−0.148045	+	0.0854741i
$935$	2.51441	−	26.0296i	0.00268921	−	0.0278392i
$936$	733.812	−	1271.00i	0.783988	−	1.35791i
$937$	−343.232	−	343.232i	−0.366310	−	0.366310i	0.499820	−	0.866129i	$-0.333400\pi$
$937$	−343.232	−	343.232i	−0.366310	−	0.366310i	−0.866129	+	0.499820i	$0.833400\pi$
$938$		0			0
$939$		−	759.087i		−	0.808400i
$940$	223.716	+	491.298i	0.237996	+	0.522658i
$941$	−556.358	−	963.640i	−0.591241	−	1.02406i	−0.994066	−	0.108783i	$-0.965305\pi$
$941$	−556.358	−	963.640i	−0.591241	−	1.02406i	0.402824	−	0.915277i	$-0.368029\pi$
$942$	132.521	−	494.577i	0.140681	−	0.525029i
$943$	−37.6737	−	140.600i	−0.0399509	−	0.149099i
$944$		−	18.3295i		−	0.0194168i
$945$		0			0
$946$	−132.847			−0.140431
$947$	1636.49	−	438.497i	1.72808	−	0.463038i	0.748341	−	0.663314i	$-0.230851\pi$
$947$	1636.49	−	438.497i	1.72808	−	0.463038i	0.979739	+	0.200277i	$0.0641841\pi$
$948$	163.561	+	43.8261i	0.172533	+	0.0462300i
$949$	−1417.58	+	818.438i	−1.49376	+	0.862421i
$950$	370.590	+	550.149i	0.390095	+	0.579104i
$951$	−2061.43			−2.16765
$952$		0			0
$953$	−892.480	+	892.480i	−0.936495	+	0.936495i	−0.998101	−	0.0616058i	$-0.980378\pi$
$953$	−892.480	+	892.480i	−0.936495	+	0.936495i	0.0616058	+	0.998101i	$0.480378\pi$
$954$	92.6634	+	53.4993i	0.0971315	+	0.0560789i
$955$	268.506	+	325.928i	0.281159	+	0.341285i
$956$	−454.416	−	787.071i	−0.475330	−	0.823296i
$957$	−180.364	+	48.3285i	−0.188469	+	0.0505000i
$958$	671.140	−	671.140i	0.700563	−	0.700563i
$959$		0			0
$960$	−736.344	−	525.569i	−0.767025	−	0.547468i
$961$	284.368	−	492.540i	0.295908	−	0.512528i
$962$	−99.8975	+	372.823i	−0.103844	+	0.387550i
$963$	−1080.06	−	289.401i	−1.12156	−	0.300520i
$964$	−576.893	−	333.069i	−0.598437	−	0.345508i
$965$	−313.205	+	438.813i	−0.324565	+	0.454729i
$966$		0			0
$967$	456.890	+	456.890i	0.472482	+	0.472482i	0.902717	−	0.430235i	$-0.141569\pi$
$967$	456.890	+	456.890i	0.472482	+	0.472482i	−0.430235	+	0.902717i	$0.641569\pi$
$968$	−179.696	−	670.634i	−0.185636	−	0.692803i
$969$	65.6914	−	37.9270i	0.0677930	−	0.0391403i
$970$	−385.767	+	317.804i	−0.397698	+	0.327633i
$971$	659.395	−	1142.11i	0.679089	−	1.17622i	−0.296167	−	0.955136i	$-0.595709\pi$
$971$	659.395	−	1142.11i	0.679089	−	1.17622i	0.975256	−	0.221080i	$-0.0709581\pi$
$972$	561.736	+	561.736i	0.577918	+	0.577918i
$973$		0			0
$974$			854.182i			0.876984i
$975$	−2223.34	−	433.586i	−2.28035	−	0.444704i
$976$	13.1326	+	22.7464i	0.0134556	+	0.0233057i
$977$	−178.032	+	664.423i	−0.182223	+	0.680065i	0.812985	+	0.582284i	$0.197841\pi$
$977$	−178.032	+	664.423i	−0.182223	+	0.680065i	−0.995208	+	0.0977804i	$0.968826\pi$
$978$	−59.3320	−	221.430i	−0.0606666	−	0.226411i
$979$		−	648.531i		−	0.662442i
$980$		0			0
$981$	−1086.47			−1.10751
$982$	75.7546	−	20.2984i	0.0771432	−	0.0206704i
$983$	−385.752	−	103.362i	−0.392423	−	0.105149i	0.0572115	−	0.998362i	$-0.481779\pi$
$983$	−385.752	−	103.362i	−0.392423	−	0.105149i	−0.449634	+	0.893213i	$0.648446\pi$
$984$	−352.843	+	203.714i	−0.358580	+	0.207026i
$985$	−315.894	+	143.844i	−0.320705	+	0.146035i
$986$	−8.41900			−0.00853854
$987$		0			0
$988$	−761.221	+	761.221i	−0.770466	+	0.770466i
$989$	182.611	+	105.431i	0.184642	+	0.106603i
$990$	−313.633	−	30.2963i	−0.316801	−	0.0306023i
$991$	352.050	+	609.769i	0.355248	+	0.615307i	0.987160	−	0.159733i	$-0.0510632\pi$
$991$	352.050	+	609.769i	0.355248	+	0.615307i	−0.631913	+	0.775040i	$0.717730\pi$
$992$	−600.781	+	160.979i	−0.605626	+	0.162277i
$993$	1364.13	−	1364.13i	1.37375	−	1.37375i
$994$		0			0
$995$	−171.657	−	1027.71i	−0.172520	−	1.03288i
$996$	30.8611	−	53.4531i	0.0309851	−	0.0536677i
$997$	190.370	−	710.472i	0.190943	−	0.712610i	−0.802336	−	0.596872i	$-0.796410\pi$
$997$	190.370	−	710.472i	0.190943	−	0.712610i	0.993280	−	0.115738i	$-0.0369233\pi$
$998$	59.5483	+	15.9559i	0.0596676	+	0.0159879i
$999$	−35.7417	−	20.6355i	−0.0357774	−	0.0206561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.3.m.b.177.3		24
5.3	odd	4	inner	245.3.m.b.128.4		24
7.2	even	3		245.3.g.b.197.4		12
7.3	odd	6		35.3.l.a.32.4	yes	24
7.4	even	3	inner	245.3.m.b.67.4		24
7.5	odd	6		245.3.g.c.197.4		12
7.6	odd	2		35.3.l.a.2.3	✓	24
21.17	even	6		315.3.ca.a.172.3		24
21.20	even	2		315.3.ca.a.37.4		24
35.3	even	12		35.3.l.a.18.3	yes	24
35.13	even	4		35.3.l.a.23.4	yes	24
35.17	even	12		175.3.p.c.18.4		24
35.18	odd	12	inner	245.3.m.b.18.3		24
35.23	odd	12		245.3.g.b.148.4		12
35.24	odd	6		175.3.p.c.32.3		24
35.27	even	4		175.3.p.c.93.3		24
35.33	even	12		245.3.g.c.148.4		12
35.34	odd	2		175.3.p.c.107.4		24
105.38	odd	12		315.3.ca.a.298.4		24
105.83	odd	4		315.3.ca.a.163.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.l.a.2.3	✓	24	7.6	odd	2
35.3.l.a.18.3	yes	24	35.3	even	12
35.3.l.a.23.4	yes	24	35.13	even	4
35.3.l.a.32.4	yes	24	7.3	odd	6
175.3.p.c.18.4		24	35.17	even	12
175.3.p.c.32.3		24	35.24	odd	6
175.3.p.c.93.3		24	35.27	even	4
175.3.p.c.107.4		24	35.34	odd	2
245.3.g.b.148.4		12	35.23	odd	12
245.3.g.b.197.4		12	7.2	even	3
245.3.g.c.148.4		12	35.33	even	12
245.3.g.c.197.4		12	7.5	odd	6
245.3.m.b.18.3		24	35.18	odd	12	inner
245.3.m.b.67.4		24	7.4	even	3	inner
245.3.m.b.128.4		24	5.3	odd	4	inner
245.3.m.b.177.3		24	1.1	even	1	trivial
315.3.ca.a.37.4		24	21.20	even	2
315.3.ca.a.163.3		24	105.83	odd	4
315.3.ca.a.172.3		24	21.17	even	6
315.3.ca.a.298.4		24	105.38	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	245.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.23172 + 0.330037i) q^{2} +(4.01589 + 1.07605i) q^{3} +(-2.05590 + 1.18698i) q^{4} +(1.75247 - 4.68282i) q^{5} -5.30157 q^{6} +(5.74725 - 5.74725i) q^{8} +(7.17525 + 4.14263i) q^{9} +O(q^{10})\)	\(q+(-1.23172 + 0.330037i) q^{2} +(4.01589 + 1.07605i) q^{3} +(-2.05590 + 1.18698i) q^{4} +(1.75247 - 4.68282i) q^{5} -5.30157 q^{6} +(5.74725 - 5.74725i) q^{8} +(7.17525 + 4.14263i) q^{9} +(-0.613038 + 6.34629i) q^{10} +(2.98240 + 5.16566i) q^{11} +(-9.53353 + 2.55450i) q^{12} +(15.4106 - 15.4106i) q^{13} +(12.0767 - 16.9200i) q^{15} +(-0.434268 + 0.752174i) q^{16} +(0.226943 - 0.846962i) q^{17} +(-10.2051 - 2.73444i) q^{18} +(18.0198 + 10.4038i) q^{19} +(1.95549 + 11.7076i) q^{20} +(-5.37832 - 5.37832i) q^{22} +(3.12465 + 11.6614i) q^{23} +(29.2647 - 16.8960i) q^{24} +(-18.8577 - 16.4130i) q^{25} +(-13.8954 + 24.0675i) q^{26} +(-2.10122 - 2.10122i) q^{27} +7.52964i q^{29} +(-9.29084 + 24.8263i) q^{30} +(9.90283 + 17.1522i) q^{31} +(-8.12792 + 30.3338i) q^{32} +(6.41844 + 23.9539i) q^{33} +1.11811i q^{34} -19.6688 q^{36} +(13.4154 - 3.59463i) q^{37} +(-25.6289 - 6.86725i) q^{38} +(78.4697 - 45.3045i) q^{39} +(-16.8415 - 36.9853i) q^{40} -12.0569 q^{41} +(12.3503 - 12.3503i) q^{43} +(-12.2630 - 7.08007i) q^{44} +(31.9736 - 26.3406i) q^{45} +(-7.69736 - 13.3322i) q^{46} +(43.9302 - 11.7711i) q^{47} +(-2.55335 + 2.55335i) q^{48} +(28.6442 + 13.9924i) q^{50} +(1.82275 - 3.15710i) q^{51} +(-13.3907 + 49.9746i) q^{52} +(-9.78248 - 2.62121i) q^{53} +(3.28158 + 1.89462i) q^{54} +(29.4164 - 4.91337i) q^{55} +(61.1707 + 61.1707i) q^{57} +(-2.48506 - 9.27437i) q^{58} +(-18.2765 + 10.5519i) q^{59} +(-4.74494 + 49.1206i) q^{60} +(15.1204 - 26.1893i) q^{61} +(-17.8583 - 17.8583i) q^{62} -43.5193i q^{64} +(-45.1584 - 99.1715i) q^{65} +(-15.8114 - 27.3861i) q^{66} +(-18.6717 + 69.6836i) q^{67} +(0.538751 + 2.01065i) q^{68} +50.1930i q^{69} -128.667 q^{71} +(65.0467 - 17.4292i) q^{72} +(-72.5481 - 19.4392i) q^{73} +(-15.3375 + 8.85513i) q^{74} +(-58.0691 - 86.2048i) q^{75} -49.3961 q^{76} +(-81.7002 + 81.7002i) q^{78} +(-14.8579 - 8.57820i) q^{79} +(2.76126 + 3.35176i) q^{80} +(-43.4609 - 75.2765i) q^{81} +(14.8507 - 3.97924i) q^{82} +(-4.42198 + 4.42198i) q^{83} +(-3.56846 - 2.54701i) q^{85} +(-11.1360 + 19.2881i) q^{86} +(-8.10230 + 30.2382i) q^{87} +(46.8289 + 12.5478i) q^{88} +(-94.1599 - 54.3633i) q^{89} +(-30.6890 + 42.9966i) q^{90} +(-20.2657 - 20.2657i) q^{92} +(21.3120 + 79.5373i) q^{93} +(-50.2247 + 28.9972i) q^{94} +(80.2982 - 66.1515i) q^{95} +(-65.2816 + 113.071i) q^{96} +(55.4317 + 55.4317i) q^{97} +49.4198i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{3} + 4 q^{5} - 36 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 + 2 * q^3 + 4 * q^5 - 36 * q^8	\( 24 q - 2 q^{2} + 2 q^{3} + 4 q^{5} - 36 q^{8} - 14 q^{10} - 24 q^{11} + 46 q^{12} + 8 q^{13} + 52 q^{15} + 20 q^{16} + 48 q^{17} - 4 q^{18} + 72 q^{20} + 104 q^{22} - 86 q^{23} - 16 q^{25} - 140 q^{26} - 76 q^{27} + 64 q^{30} - 120 q^{31} + 130 q^{32} - 116 q^{33} - 496 q^{36} + 44 q^{37} - 16 q^{38} + 158 q^{40} - 16 q^{41} - 196 q^{43} + 104 q^{45} - 148 q^{46} + 208 q^{47} + 52 q^{48} + 580 q^{50} - 160 q^{51} + 288 q^{52} - 72 q^{53} - 208 q^{55} + 656 q^{57} - 2 q^{58} + 262 q^{60} - 308 q^{61} - 176 q^{62} + 132 q^{65} - 316 q^{66} + 198 q^{67} - 332 q^{68} - 792 q^{71} + 308 q^{72} - 380 q^{73} + 450 q^{75} + 400 q^{76} - 720 q^{78} + 324 q^{80} - 352 q^{81} + 818 q^{82} + 460 q^{83} + 144 q^{85} - 336 q^{86} + 214 q^{87} - 288 q^{88} - 120 q^{90} + 1372 q^{92} - 68 q^{93} - 88 q^{95} - 816 q^{96} + 72 q^{97}+O(q^{100}) \) 24 * q - 2 * q^2 + 2 * q^3 + 4 * q^5 - 36 * q^8 - 14 * q^10 - 24 * q^11 + 46 * q^12 + 8 * q^13 + 52 * q^15 + 20 * q^16 + 48 * q^17 - 4 * q^18 + 72 * q^20 + 104 * q^22 - 86 * q^23 - 16 * q^25 - 140 * q^26 - 76 * q^27 + 64 * q^30 - 120 * q^31 + 130 * q^32 - 116 * q^33 - 496 * q^36 + 44 * q^37 - 16 * q^38 + 158 * q^40 - 16 * q^41 - 196 * q^43 + 104 * q^45 - 148 * q^46 + 208 * q^47 + 52 * q^48 + 580 * q^50 - 160 * q^51 + 288 * q^52 - 72 * q^53 - 208 * q^55 + 656 * q^57 - 2 * q^58 + 262 * q^60 - 308 * q^61 - 176 * q^62 + 132 * q^65 - 316 * q^66 + 198 * q^67 - 332 * q^68 - 792 * q^71 + 308 * q^72 - 380 * q^73 + 450 * q^75 + 400 * q^76 - 720 * q^78 + 324 * q^80 - 352 * q^81 + 818 * q^82 + 460 * q^83 + 144 * q^85 - 336 * q^86 + 214 * q^87 - 288 * q^88 - 120 * q^90 + 1372 * q^92 - 68 * q^93 - 88 * q^95 - 816 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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